The generator matrix
1 0 0 1
0 1 0 1
0 0 1 1
0 0 0 2X
generates a code of length 4 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+172x^2+1344x^3+5158x^4+1344x^5+172x^6+1x^8
The gray image is a code over GF(2) with n=32, k=13 and d=8.
This code was found by Heurico 1.16 in 0.016 seconds.