The generator matrix

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

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+165x^68+136x^69+312x^70+240x^71+500x^72+248x^73+364x^74+288x^75+398x^76+248x^77+370x^78+240x^79+267x^80+136x^81+74x^82+48x^84+18x^86+22x^88+10x^90+3x^92+4x^94+2x^96+1x^100+1x^108

The gray image is a linear code over GF(2) with n=300, k=12 and d=136.
This code was found by Heurico 1.16 in 1.17 seconds.