The generator matrix
1 0 1 X
0 1 1 2X+2
0 0 X X
0 0 0 2X
generates a code of length 4 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+124x^2+768x^3+2310x^4+768x^5+124x^6+1x^8
The gray image is a code over GF(2) with n=32, k=12 and d=8.
This code was found by Heurico 1.16 in 1.05e-007 seconds.