The generator matrix
1 0 1 1 1 0 1 1 2 1 1 0 0 X 0 2 1 1
0 1 1 0 1 1 0 X+1 1 1 X 1 1 X 0 1 2 0
0 0 X 0 0 0 X+2 2 X 0 0 X 0 2 X 2 X 0
0 0 0 X 0 0 0 0 X X+2 2 X X 0 2 X X+2 X+2
0 0 0 0 X X+2 0 2 X+2 2 X 0 X X+2 2 2 X X
0 0 0 0 0 2 0 0 0 0 0 2 2 0 2 2 2 0
0 0 0 0 0 0 2 2 2 2 2 0 2 0 0 0 0 0
generates a code of length 18 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+213x^12+104x^13+764x^14+784x^15+2275x^16+2168x^17+3672x^18+2208x^19+2400x^20+792x^21+732x^22+80x^23+156x^24+8x^25+16x^26+11x^28
The gray image is a code over GF(2) with n=72, k=14 and d=24.
This code was found by Heurico 1.16 in 89.2 seconds.