The generator matrix
1 1 1 1
0 X 0 2X
0 0 2 0
0 0 0 2X+2
generates a code of length 4 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 1.
Homogenous weight enumerator: w(x)=1x^0+12x^1+52x^2+180x^3+1558x^4+180x^5+52x^6+12x^7+1x^8
The gray image is a code over GF(2) with n=32, k=11 and d=4.
This code was found by Heurico 1.16 in -3.24e-008 seconds.