The generator matrix
1 1 1 1 X 2X 1 1 X
0 X 0 3X+2 X+2 X 2X+2 3X 3X+2
0 0 2X+2 0 2X 0 2 2 2
0 0 0 2X+2 2X 2X+2 2 2X+2 0
generates a code of length 9 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+58x^6+104x^7+521x^8+688x^9+508x^10+104x^11+62x^12+2x^14
The gray image is a code over GF(2) with n=72, k=11 and d=24.
This code was found by Heurico 1.16 in 0.016 seconds.