The generator matrix
1 0 1 1
0 1 0 2X
0 0 2X+2 0
0 0 0 2
generates a code of length 4 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 1.
Homogenous weight enumerator: w(x)=1x^0+20x^1+100x^2+428x^3+2998x^4+428x^5+100x^6+20x^7+1x^8
The gray image is a code over GF(2) with n=32, k=12 and d=4.
This code was found by Heurico 1.16 in 6.87e-008 seconds.