The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  1  1  1  1 X^2  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2  0 X^2 X^2  0  0 X^3 X^3  0 X^3 X^2 X^3+X^2  0  0
 0  0 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3  0 X^3+X^2 X^2  0 X^2 X^2  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3  0  0 X^3 X^3  0  0 X^2 X^2  0 X^3+X^2 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+9x^36+64x^37+109x^38+60x^39+6x^40+2x^41+3x^42+2x^53

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 0.015 seconds.