The generator matrix

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

generates a code of length 11 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+13x^8+126x^9+186x^10+398x^11+160x^12+106x^13+22x^14+10x^15+2x^16

The gray image is a code over GF(2) with n=88, k=10 and d=32.
This code was found by Heurico 1.16 in 0.016 seconds.