The generator matrix

 1  1  X  1
 0  X  X  0
 0  0 2X+2 2X

generates a code of length 4 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+16x^2+80x^3+318x^4+80x^5+16x^6+1x^8

The gray image is a code over GF(2) with n=32, k=9 and d=8.
This code was found by Heurico 1.16 in -3.24e-008 seconds.