The generator matrix

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

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+30x^10+64x^11+31x^12+1x^14+1x^18

The gray image is a code over GF(2) with n=88, k=7 and d=40.
This code was found by Heurico 1.16 in 0 seconds.