The generator matrix
1 0 0 1 1 1 3X+2 1 1
0 1 0 1 2 3 1 X 0
0 0 1 1 0 X+1 X 2X+1 0
0 0 0 X 3X+2 2X+2 3X 0 2X
generates a code of length 9 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 5.
Homogenous weight enumerator: w(x)=1x^0+96x^5+434x^6+1554x^7+6710x^8+15144x^9+6780x^10+1532x^11+408x^12+104x^13+2x^14+2x^15+1x^16
The gray image is a code over GF(2) with n=72, k=15 and d=20.
This code was found by Heurico 1.16 in 0.531 seconds.