The generator matrix

 1  1  X  X
 0  X  X  2
 0  0 X^2 X^2
 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+52x^2+160x^3+598x^4+160x^5+52x^6+1x^8

The gray image is a code over GF(2) with n=32, k=10 and d=8.
This code was found by Heurico 1.16 in -3.24e-008 seconds.