The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^3  1  1  1  1  X  1  1  0  1  1  X  1  1  X  0  1  1  1 X^2  1  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X X^2 X^2+X  0 X^2+X X^3 X^3+X X^2 X^2+X  X  X  0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X  0  X X^2 X^3+X X^3+X^2+X  0 X^3+X  X  0 X^3+X X^3+X^2+X X^2+X  X X^3 X^3+X^2+X
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^2 X^2  0 X^3 X^3+X^2 X^2 X^2 X^3  0 X^3 X^3+X^2  0  0 X^3 X^3 X^3+X^2 X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3+X^2  0 X^3 X^2 X^3 X^2
 0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3
 0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  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+112x^35+115x^36+326x^37+289x^38+454x^39+271x^40+268x^41+52x^42+92x^43+29x^44+14x^45+9x^46+14x^47+1x^54+1x^62

The gray image is a linear code over GF(2) with n=312, k=11 and d=140.
This code was found by Heurico 1.16 in 2.5 seconds.