The generator matrix

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

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+37x^8+260x^9+376x^10+718x^11+378x^12+218x^13+40x^14+18x^15+2x^17

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.