The generator matrix
1 0 1 1 1 3X 1 1 1
0 1 1 2 3X+1 1 3X+3 3X+3 0
0 0 X 3X+2 2X+2 3X+2 X 2X+2 2X
0 0 0 2X 0 0 2X 2X 2X
generates a code of length 9 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+57x^6+220x^7+807x^8+1936x^9+804x^10+204x^11+56x^12+8x^13+3x^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 0.016 seconds.