The generator matrix

 1  0  0  1  1  1  1  1
 0  1  0  1 X+2 X+3  2  2
 0  0  1  1 X+1  X X+2  2

generates a code of length 8 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+8x^5+64x^6+98x^7+189x^8+70x^9+64x^10+14x^11+2x^12+2x^13

The gray image is a code over GF(2) with n=32, k=9 and d=10.
This code was found by Heurico 1.13 in -9.54e-008 seconds.