The generator matrix

 1  0  0  0  1  1  1 X+2  1  1  1
 0  1  0  0  X X^2+1  1  1 X+1 X+3  0
 0  0  1  0 X+1  1  X X+1  3 X^2+2 X^2
 0  0  0  1  1  X X+1 X^2+1 X^2+3 X^2+X 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+132x^7+1057x^8+4706x^9+14575x^10+24432x^11+14910x^12+4588x^13+942x^14+188x^15+2x^17+3x^18

The gray image is a code over GF(2) with n=88, k=16 and d=28.
This code was found by Heurico 1.16 in 3.02 seconds.