The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+98x^8+64x^9+528x^10+640x^11+584x^12+64x^13+48x^14+21x^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 0.781 seconds.