The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 X X 1 X X^2 X X 1 X^2 X X X^2 X^3 0 1 X^2 X X^3 1
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 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 0
generates a code of length 38 over Z2[X]/(X^4) who´s minimum homogenous weight is 38.
Homogenous weight enumerator: w(x)=1x^0+1x^38+26x^39+1x^40+2x^41+1x^42
The gray image is a linear code over GF(2) with n=304, k=5 and d=152.
This code was found by Heurico 1.16 in 0.016 seconds.