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

generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+182x^68+144x^70+387x^72+330x^74+444x^76+214x^78+182x^80+58x^82+60x^84+18x^86+20x^88+4x^90+2x^92+1x^96+1x^120

The gray image is a linear code over GF(2) with n=300, k=11 and d=136.
This code was found by Heurico 1.16 in 0.683 seconds.