The generator matrix
1 1 1 1 1 1 1 1 X X X X X^2 1 0 1 X^2 2 1
0 X^2+2 2 X^2 0 X^2+2 2 X^2 X^2+2 X^2 0 2 X^2+2 0 X^2 2 X^2 X^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+2x^18+54x^19+3x^20+1x^22+2x^23+1x^26
The gray image is a code over GF(2) with n=152, k=6 and d=72.
This code was found by Heurico 1.16 in -6.48e-008 seconds.