The generator matrix
1 0 0 1
0 1 0 2X
0 0 1 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+32x^1+364x^2+2336x^3+10918x^4+2336x^5+364x^6+32x^7+1x^8
The gray image is a code over GF(2) with n=32, k=14 and d=4.
This code was found by Heurico 1.16 in 0.015 seconds.