The generator matrix
1 1 1 1
0 X 2X+2 X+2
generates a code of length 4 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+16x^3+94x^4+16x^5+1x^8
The gray image is a code over GF(2) with n=32, k=7 and d=12.
This code was found by Heurico 1.16 in -6.48e-008 seconds.