The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3  1  1 X^3+X^2+X  1 X^3+X^2  1  1  X  1 X^2 X^3+X  1  1  1  1  1  1  0  0  1  1  X  1  1 X^2  1  1 X^2+X  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+1 X^3  1 X^2+X+1 X^3+X^2+X  1 X^2  1 X^3+X^2+1 X^3+X  1 X+1  1  1 X^3+X^2 X^3+X^2+X+1  X  1  0  0  1  1 X^3+X^2+1 X+1 X^3+X X^3+X^2+X+1 X^2  1  X X^2+X+1  1 X^3+1 X^2+X+1
 0  0 X^2  0 X^3  0 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0 X^3+X^2 X^3 X^2  0 X^2 X^3  0 X^3 X^2 X^3+X^2  0 X^2  0 X^2 X^3+X^2 X^3 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3  0 X^2 X^2
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  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+240x^36+232x^37+504x^38+184x^39+450x^40+216x^41+152x^42+8x^43+50x^44+9x^48+2x^52

The gray image is a linear code over GF(2) with n=312, k=11 and d=144.
This code was found by Heurico 1.16 in 0.125 seconds.