The generator matrix

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

generates a code of length 39 over Z2[X]/(X^4) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+94x^36+88x^37+280x^38+144x^39+215x^40+88x^41+110x^42+2x^50+2x^56

The gray image is a linear code over GF(2) with n=312, k=10 and d=144.
This code was found by Heurico 1.16 in 0.329 seconds.