The generator matrix
1 1 1 1
0 X 0 X
0 0 X X
0 0 0 2
generates a code of length 4 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+76x^2+192x^3+1510x^4+192x^5+76x^6+1x^8
The gray image is a code over GF(2) with n=32, k=11 and d=8.
This code was found by Heurico 1.16 in -1.01e-007 seconds.