The generator matrix

 1  1  1  1  0  1  1 2X  X  1  1
 0  X  0  X  X 2X  2  2 3X 2X 2X
 0  0  X  X 2X+2  2  X  X X+2 2X 3X+2
 0  0  0 2X  0 2X  0 2X 2X  0  0
 0  0  0  0 2X 2X 2X 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+194x^8+192x^9+944x^10+1408x^11+1000x^12+192x^13+144x^14+21x^16

The gray image is a code over GF(2) with n=88, k=12 and d=32.
This code was found by Heurico 1.16 in 20.1 seconds.