The generator matrix

 1  0  1  1  1 3X  1  0  1  X  1
 0  1  1  2 3X+1  1  X  0 3X  0 2X
 0  0  X 3X+2 2X+2 3X+2 3X  X 3X+2 2X+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+29x^8+216x^9+368x^10+832x^11+390x^12+152x^13+40x^14+16x^15+4x^16

The gray image is a code over GF(2) with n=88, k=11 and d=32.
This code was found by Heurico 1.16 in 0.015 seconds.