The generator matrix

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

generates a code of length 11 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+98x^7+591x^8+2576x^9+7285x^10+11588x^11+7466x^12+2496x^13+522x^14+138x^15+6x^16+1x^18

The gray image is a code over GF(2) with n=88, k=15 and d=28.
This code was found by Heurico 1.16 in 0.797 seconds.