The generator matrix

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

generates a code of length 38 over Z2[X]/(X^4) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+6x^36+84x^37+77x^38+72x^39+8x^40+4x^41+2x^42+1x^48+1x^54

The gray image is a linear code over GF(2) with n=304, k=8 and d=144.
This code was found by Heurico 1.16 in 0.031 seconds.