The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+112x^8+128x^9+138x^10+1280x^11+164x^12+128x^13+84x^14+11x^16+2x^18

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 -1.01e-007 seconds.