The generator matrix

 1  0  1  1  1  1 X+2  1  1  1  X
 0  1 X+1 X+2 3X+3  3  1 2X+1 X+1  3  0
 0  0 2X  0  0  0  0 2X  0 2X 2X
 0  0  0 2X  0  0 2X 2X  0 2X  0
 0  0  0  0 2X  0  0 2X 2X  0 2X
 0  0  0  0  0 2X  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+98x^8+256x^9+1040x^10+1280x^11+1096x^12+256x^13+48x^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 15.5 seconds.