The generator matrix
1 1 1 1
0 X^3 0 0
0 0 X^3 0
0 0 0 X^3
generates a code of length 4 over Z2[X]/(X^4) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+4x^2+118x^4+4x^6+1x^8
The gray image is a linear code over GF(2) with n=32, k=7 and d=8.
This code was found by Heurico 1.16 in -1.01e-007 seconds.