The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1
0 2X 0 0 0 0 0 0 2X 0 2X 2X 0 2X 2X 0 0 2X
0 0 2X 0 0 0 0 0 2X 2X 2X 0 2X 2X 0 0 2X 2X
0 0 0 2X 0 0 0 2X 0 2X 0 2X 2X 2X 0 0 0 2X
0 0 0 0 2X 0 0 2X 0 0 2X 2X 2X 0 2X 0 2X 2X
0 0 0 0 0 2X 0 2X 2X 0 2X 0 0 2X 2X 2X 2X 0
0 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 0
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+33x^14+45x^16+96x^17+768x^18+32x^21+30x^22+18x^24+1x^30
The gray image is a code over GF(2) with n=144, k=10 and d=56.
This code was found by Heurico 1.16 in 0.016 seconds.