The generator matrix

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

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+96x^8+768x^9+1512x^10+3472x^11+1484x^12+736x^13+104x^14+16x^15+3x^16

The gray image is a code over GF(2) with n=88, k=13 and d=32.
This code was found by Heurico 1.16 in 0.062 seconds.