The generator matrix

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

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+38x^34+60x^35+219x^36+44x^37+423x^38+392x^39+567x^40+72x^41+110x^42+60x^43+45x^44+12x^45+4x^46+1x^70

The gray image is a linear code over GF(2) with n=312, k=11 and d=136.
This code was found by Heurico 1.16 in 0.094 seconds.