The generator matrix

 1  1  1  1  1  1  X 2X  1  1  X
 0  X  0 X+2  2 2X+2 3X+2  X  0 3X+2 3X+2
 0  0 2X+2  0  2 2X  2 2X+2 2X 2X+2 2X+2
 0  0  0 2X  0 2X  0 2X  0 2X  0
 0  0  0  0 2X  0  0 2X 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+72x^8+160x^9+376x^10+832x^11+380x^12+160x^13+56x^14+11x^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 0.016 seconds.