The generator matrix
1 1 1 1 1 1 1 1 1 X X 1 2X+2 0 2X 1 1 1
0 X 0 X 0 2X X+2 2 X+2 0 3X+2 2X+2 X X 2 3X 2X X+2
0 0 X X 2X+2 3X+2 X+2 2X+2 2X X+2 2 0 X+2 0 X 3X 3X+2 0
0 0 0 2X 0 0 0 2X 2X 2X 0 0 0 2X 2X 2X 2X 0
0 0 0 0 2X 2X 0 0 2X 2X 0 2X 0 2X 0 2X 0 2X
generates a code of length 18 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 14.
Homogenous weight enumerator: w(x)=1x^0+83x^14+150x^15+554x^16+568x^17+1420x^18+540x^19+550x^20+136x^21+63x^22+14x^23+15x^24+2x^26
The gray image is a code over GF(2) with n=144, k=12 and d=56.
This code was found by Heurico 1.16 in 0.062 seconds.