The generator matrix

 1  1  1  1  1  1  X  X  X  X  X
 0  X  0  X 2X  0  X 3X+2 2X+2 2X  2
 0  0  X  X 2X+2 3X+2  X 2X+2  X  0 X+2
 0  0  0 2X+2  0 2X  0 2X+2 2X  2  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+196x^8+352x^9+800x^10+1360x^11+892x^12+320x^13+144x^14+16x^15+15x^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 0.782 seconds.