The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1 1 X X X 1 1 X X^2 X^2 X^2 X 1 1 X^3 X^3 0 0 X^2 X X
0 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 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 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 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+52x^38+6x^40+4x^42+1x^48
The gray image is a linear code over GF(2) with n=304, k=6 and d=152.
This code was found by Heurico 1.16 in 0.032 seconds.