The generator matrix

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

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+98x^8+160x^9+1128x^10+1344x^11+1104x^12+160x^13+88x^14+13x^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 0.031 seconds.