The generator matrix

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

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+53x^36+258x^37+96x^38+246x^39+81x^40+206x^41+47x^42+26x^43+8x^44+1x^50+1x^60

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 0.031 seconds.