The generator matrix

 1  1  1  1  1  1  1  1  X  X  0
 0  X X^2+2 X^2+X  0 X^2+X+2  2 X+2 X^2 X^2+X  X
 0  0  2  2  2  2  2  2  2  2  2

generates a code of length 11 over Z4[X]/(X^3+2,2X) 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 0.016 seconds.