The generator matrix

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

generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+252x^70+516x^72+428x^74+300x^76+234x^78+127x^80+88x^82+68x^84+14x^86+8x^88+8x^90+4x^92

The gray image is a linear code over GF(2) with n=300, k=11 and d=140.
This code was found by Heurico 1.11 in 0.281 seconds.