The generator matrix
1 1 1 1 1 1 1 1 X X 1 1 X 1 1 X X X X
0 2 0 0 0 2 2 2 0 0 0 2 2 0 2 0 2 2 2
0 0 2 0 2 2 2 0 0 2 0 2 2 2 2 2 0 2 0
0 0 0 2 2 0 2 2 2 2 0 0 0 0 2 0 2 2 0
generates a code of length 19 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+18x^18+96x^19+6x^20+4x^22+1x^24+2x^26
The gray image is a code over GF(2) with n=152, k=7 and d=72.
This code was found by Heurico 1.16 in 1.05e-007 seconds.