The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+17x^8+122x^9+182x^10+402x^11+156x^12+110x^13+26x^14+6x^15+2x^16

The gray image is a code over GF(2) with n=88, k=10 and d=32.
This code was found by Heurico 1.16 in 0.015 seconds.