The generator matrix

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

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+66x^8+32x^9+48x^10+704x^11+104x^12+32x^13+16x^14+21x^16

The gray image is a code over GF(2) with n=88, k=10 and d=32.
This code was found by Heurico 1.16 in 0.078 seconds.