The generator matrix

 1  0  1  1
 0  1  1  2
 0  0  X X^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+288x^3+1366x^4+288x^5+52x^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 3.81e-009 seconds.