The generator matrix

 1  1  1  1  X  0  1  1  1  1  X
 0  X 2X+2 X+2 X+2  X  0  0 2X+2 2X+2 2X+2
 0  0 2X  0  0 2X  0 2X  0 2X  0
 0  0  0 2X  0 2X 2X 2X  0  0  0
 0  0  0  0 2X 2X  0  0 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+44x^8+32x^9+272x^10+320x^11+284x^12+32x^13+32x^14+7x^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 0.015 seconds.