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

generates a code of length 39 over Z2[X]/(X^4) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+35x^34+200x^35+135x^36+736x^37+349x^38+1200x^39+345x^40+736x^41+118x^42+200x^43+29x^44+6x^46+2x^48+2x^50+1x^58+1x^62

The gray image is a linear code over GF(2) with n=312, k=12 and d=136.
This code was found by Heurico 1.16 in 0.141 seconds.