The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X^2 X X
0 X^2+2 0 X^2+2 0 X^2+2 2 X^2 0 X^2+2 2 X^2 2 X^2 2 X^2 X^2+2 X^2+2 0 0
0 0 2 0 0 2 2 2 2 2 2 0 0 2 0 0 0 0 2 0
0 0 0 2 2 2 2 0 2 0 0 2 2 2 0 0 0 2 2 0
generates a code of length 20 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+16x^18+64x^19+92x^20+64x^21+16x^22+2x^24+1x^32
The gray image is a code over GF(2) with n=160, k=8 and d=72.
This code was found by Heurico 1.16 in -1.01e-007 seconds.