The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+103x^10+64x^11+78x^12+8x^14+1x^16+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 0.015 seconds.