The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 1 1 X 1 X X X 1 1 X^2 0 X^2 2 1 X X X^2 X X X^2 X X 1 1
0 X^2+2 2 X^2 0 X^2+2 2 X^2 0 X^2+2 2 X^2 X^2+2 X^2 0 2 X^2+2 X^2 X^2+2 0 2 0 X^2 2 X^2+2 X^2+2 X^2 X^2 X^2 X^2 0 2 2 X^2+2 X^2 0 0 2 0 2
generates a code of length 40 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+49x^40+10x^42+2x^44+2x^46
The gray image is a code over GF(2) with n=320, k=6 and d=160.
This code was found by Heurico 1.16 in 0.016 seconds.