The generator matrix
1 0 1 1 1 3X+2 1 1 1
0 1 X+1 3X+2 3 1 0 X+2 0
0 0 2 0 2X+2 2X 2 2X+2 0
0 0 0 2X+2 2X+2 2X+2 2 2 2X
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+61x^6+172x^7+965x^8+1708x^9+958x^10+164x^11+58x^12+4x^13+5x^14
The gray image is a code over GF(2) with n=72, k=12 and d=24.
This code was found by Heurico 1.16 in 0.015 seconds.