The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+86x^10+80x^11+87x^12+1x^14+1x^18

The gray image is a code over GF(2) with n=88, k=8 and d=40.
This code was found by Heurico 1.16 in 3.81e-009 seconds.