The generator matrix
1 0 1 1
0 1 X+1 3X+2
generates a code of length 4 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+52x^3+149x^4+52x^5+2x^6
The gray image is a code over GF(2) with n=32, k=8 and d=12.
This code was found by Heurico 1.16 in -3.24e-008 seconds.