The generator matrix

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

generates a code of length 11 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+22x^9+174x^10+116x^11+175x^12+22x^13+1x^14+1x^18

The gray image is a code over GF(2) with n=88, k=9 and d=36.
This code was found by Heurico 1.16 in 3.62e-008 seconds.