The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+92x^9+250x^10+368x^11+214x^12+76x^13+14x^14+8x^15+1x^16

The gray image is a code over GF(2) with n=88, k=10 and d=36.
This code was found by Heurico 1.16 in -8.01e-008 seconds.