The generator matrix
1 1 X 1
0 2 2 0
0 0 2X 0
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+8x^2+32x^3+174x^4+32x^5+8x^6+1x^8
The gray image is a code over GF(2) with n=32, k=8 and d=8.
This code was found by Heurico 1.16 in -6.48e-008 seconds.