The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  1  1  X X^3+X^2  X X^3  X X^2  X  X  X  X  1  1  1  1  1  1  1  1  X  1
 0  X X^3+X^2 X^2+X X^3 X^3+X^2+X X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X X^3 X^2+X X^3+X^2+X  X X^2  X X^3+X  X X^3+X^2+X  X  X  X  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^2+X X^3+X X^3 X^2 X^3+X^2+X  X X^2+X  0

generates a code of length 38 over Z2[X]/(X^4) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+18x^37+84x^38+18x^39+2x^41+1x^42+2x^43+1x^44+1x^50

The gray image is a linear code over GF(2) with n=304, k=7 and d=148.
This code was found by Heurico 1.16 in 0.031 seconds.