The generator matrix

 1  1  1  1  1  1  1  1 2X+2 2X  1
 0  X  2 3X+2  0 3X+2  0 3X+2  2 2X  0
 0  0 2X  0  0 2X 2X 2X  0 2X  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+17x^8+88x^9+77x^10+152x^11+86x^12+72x^13+2x^14+8x^15+8x^16+1x^18

The gray image is a code over GF(2) with n=88, k=9 and d=32.
This code was found by Heurico 1.16 in 3.62e-008 seconds.