The generator matrix
1 1 1 1
0 X^2+2 2 X^2
generates a code of length 4 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+62x^4+1x^8
The gray image is a code over GF(2) with n=32, k=6 and d=16.
This code was found by Heurico 1.16 in 0 seconds.