The generator matrix

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

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+41x^8+42x^9+279x^10+304x^11+278x^12+36x^13+38x^14+2x^17+3x^18

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.