The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 X 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 2X 1 1 X 1 1 1 2X 2X 1 0 1 1 1 1 2X 1 1 1 1 X X 1 0 2X 1 1 X 0 2X 1 1 1 1 1 1 1 0 1 0
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 2X+1 0 2 1 2 1 0 2X+1 X 2 1 2X+1 1 X+2 2X 1 0 2X+1 2 1 0 X+2 2X+1 2X 1 1 1 1 2X+2 1 0 X+2 1 1 1 X+1 1 X 2X 2X+1 2X 1 2X X 2X+2 2X+2 1 1 X+2 1 1 0 X+2 0 1 1 2X+2 X+1 2X+1 2X+1 2 2X+1 X+2 1 0 1
0 0 2X 0 0 0 0 0 0 2X X 0 X X 2X X 0 2X 2X 2X X X 2X 2X X X 0 0 X 2X 0 X 2X 2X X 2X X 0 2X 0 X X 0 2X 0 X X 2X 0 2X 2X X 0 2X X 2X 0 X X 2X X 2X X 2X 2X 0 X 0 2X X 2X 2X 2X 0 X 2X 2X 0 2X 0 2X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X X X X 2X 2X 2X X 0 2X 2X 2X 0 2X X 2X X 2X 2X X X X 0 0 2X 0 X 2X 0 0 X 0 0 2X X 2X X X X X 0 X 2X 0 X X X X 2X X X X 0 X 2X 2X 0 0 0 X 0 2X X 2X 2X
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X 2X X X X 2X 2X X X 2X X X X X 2X X X X 0 0 2X 2X 2X 2X 2X 0 2X X X 2X X 0 0 2X X X X X 0 2X X 0 2X 0 X 0 X 2X X 2X 0 X 0 2X 2X 2X 0
0 0 0 0 0 2X 0 0 0 0 0 2X 0 X 0 0 0 X X 0 X X 2X 0 0 0 0 X 2X X 2X X 0 X X X 2X 2X 2X 2X 2X X 2X X 0 0 2X 2X X 0 X X 0 0 X X 2X 2X 0 2X 0 0 X 0 2X 2X 2X 2X X X 0 2X X X 0 2X 2X 2X 2X 0 2X 0
0 0 0 0 0 0 X 0 2X 2X X 0 0 2X 2X 2X X 0 2X 0 2X X 0 X 0 0 2X 2X 0 0 X 0 2X 2X 2X 2X X 0 0 X 2X X 0 0 0 0 2X X X X X X 2X X 0 0 X 0 2X X 0 2X 0 0 2X X X 2X X 0 2X 2X 0 X X 0 X X X 2X 0 0
0 0 0 0 0 0 0 X X 2X 0 X 2X X X X X 2X X 0 0 0 2X X X X X 0 0 0 0 0 0 X X X X 2X 0 X 2X 2X 2X X 2X 0 0 0 0 2X X X 0 X 2X X 0 X 0 X 0 X X 2X 2X 0 X 2X X 0 X 2X 0 0 2X 2X 2X 0 X 2X 2X X
generates a code of length 82 over Z3[X]/(X^2) who´s minimum homogenous weight is 141.
Homogenous weight enumerator: w(x)=1x^0+120x^141+386x^144+54x^145+558x^147+492x^148+726x^150+1050x^151+1176x^153+2214x^154+1584x^156+3738x^157+2102x^159+5628x^160+2776x^162+7176x^163+2668x^165+7212x^166+2440x^168+5898x^169+1950x^171+3576x^172+1166x^174+1662x^175+854x^177+546x^178+502x^180+102x^181+274x^183+18x^184+214x^186+88x^189+62x^192+20x^195+4x^198+4x^201+4x^204+2x^207+2x^210
The gray image is a linear code over GF(3) with n=246, k=10 and d=141.
This code was found by Heurico 1.16 in 76.5 seconds.