The generator matrix
1 1 1 1 1 1 1 1 X X X X X X X X 1 1 X
0 X^2+2 0 X^2+2 2 X^2 2 X^2 X^2+2 X^2+2 0 2 X^2 X^2 0 2 0 X^2+2 X^2+2
0 0 2 2 2 2 0 0 0 2 2 2 2 0 0 0 0 0 2
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+23x^18+80x^19+21x^20+1x^22+2x^28
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 3.62e-008 seconds.