The generator matrix

 1  0  0  1  1  1  X  1  1  X  1
 0  1  0  X 2X+3 3X+3  1 3X+2  2  0 2X
 0  0  1  1 X+1  X  1 X+3 2X+1 3X+2 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+65x^8+404x^9+728x^10+1668x^11+846x^12+284x^13+80x^14+12x^15+8x^16

The gray image is a code over GF(2) with n=88, k=12 and d=32.
This code was found by Heurico 1.16 in 0.015 seconds.