The generator matrix

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

generates a code of length 39 over Z2[X]/(X^4) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+216x^35+853x^36+1116x^37+1344x^38+1428x^39+1367x^40+824x^41+534x^42+252x^43+177x^44+52x^45+10x^46+16x^47+2x^48

The gray image is a linear code over GF(2) with n=312, k=13 and d=140.
This code was found by Heurico 1.16 in 0.781 seconds.