The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 X 0 0 0 0 0 X a*X X a^2*X a*X X X 0
0 0 X 0 0 0 X a^2*X a*X a^2*X X a*X a^2*X X 0
0 0 0 X 0 0 a^2*X 0 a^2*X X X a*X 0 a*X 0
0 0 0 0 X 0 X X a*X a*X 0 0 a*X a^2*X 0
0 0 0 0 0 X a^2*X X a^2*X 0 0 X a^2*X a^2*X 0
generates a code of length 15 over F4[X]/(X^2) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+93x^28+246x^32+360x^36+579x^40+852x^44+12288x^45+945x^48+636x^52+309x^56+75x^60
The gray image is a linear code over GF(4) with n=60, k=7 and d=28.
This code was found by Heurico 1.16 in 0.292 seconds.