The generator matrix

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

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+60x^9+142x^10+144x^11+94x^12+44x^13+18x^14+8x^15+1x^16

The gray image is a code over GF(2) with n=88, k=9 and d=36.
This code was found by Heurico 1.16 in -1.01e-007 seconds.