The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 X X X X^2 1 X 1 X X^2 X X X^2 X^3 0 X X^2 X^3 X^2 X^2
0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 0
generates a code of length 39 over Z2[X]/(X^4) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+27x^40+4x^42
The gray image is a linear code over GF(2) with n=312, k=5 and d=160.
This code was found by Heurico 1.16 in 0.015 seconds.