The generator matrix
1 0 0 0 1 1 1 1 1 1 1
0 1 0 0 X+1 X^2+X X^2 1 X^2+1 X+3 0
0 0 1 0 1 X^2 X+1 X X^2+X+1 X+1 0
0 0 0 1 1 X^2+X+1 X X+1 X X^2+X+1 0
0 0 0 0 2 2 2 0 0 0 0
generates a code of length 11 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+79x^6+656x^7+2904x^8+9954x^9+27974x^10+47896x^11+28041x^12+9964x^13+2859x^14+648x^15+93x^16+2x^17+1x^20
The gray image is a code over GF(2) with n=88, k=17 and d=24.
This code was found by Heurico 1.16 in 8.11 seconds.