The generator matrix

 1  0  0  1  1  1 X^2+X  1  X  1 X^2 X^2+X  1  1  0  1 X^2+X  1  1  X  1  X  0 X^2  1  1  1  1 X^2  1  1  0 X^2+X  1  0  1  1 X^2  1  1 X^2+X  1  1 X^2  1  1  1  X X^2  1 X^2+X  1  1  1  1  1  1 X^2  1  1  1  1 X^2  1  1 X^2+X  1  1 X^2+X X^2+X X^2  1  X  1  1
 0  1  0  0  1 X+1  1 X^2+1 X^2 X+1  1  1 X^2 X^2  X X+1  1 X^2+X X+1  1 X^2+X  0  1  1 X^2+X  X X^2+X+1  1  1  0 X^2+X+1 X^2+X  1 X^2+1  1 X^2+X X^2+1  1  1  X  X X^2+1  0 X^2+X X^2+X X^2+X+1 X^2+1  1 X^2+X  X  1 X^2+X+1 X^2+X X^2+X+1 X^2+1 X+1 X^2+X+1  1  0 X^2+X+1 X^2+X+1 X^2+X  1 X^2 X^2  1 X+1 X^2 X^2+X  1  1  1  1  X  0
 0  0  1  1 X+1 X^2  1  1  1 X^2+X  X X^2+X+1 X^2+X X+1  1 X+1 X+1 X^2+X+1 X^2+X  0  0  1  X  1  X X^2+X+1 X^2+1  0 X+1  1 X^2+X+1  1  X X^2+X  0  X  X X^2  1  1  1 X+1  X  1  X X^2+1 X^2+1 X^2+X  1  1  1 X^2 X^2+X X^2+1 X+1 X^2+X+1 X^2 X^2+1 X^2 X^2+X+1 X^2+X X^2+1 X^2+X+1  1 X^2+1 X^2+X+1 X+1 X^2+1  1 X+1  1  X  1  1  0
 0  0  0  X  X  0 X^2+X X^2+X  X X^2  0 X^2+X  0 X^2+X  X X^2  0  0  X  X X^2+X X^2 X^2+X  0 X^2+X  X X^2+X X^2 X^2+X  0 X^2 X^2 X^2 X^2  X  0  X  0 X^2+X X^2 X^2+X  0 X^2+X  X X^2  0 X^2  0 X^2  0  0 X^2+X  X  X X^2 X^2+X  X X^2+X X^2 X^2+X X^2  0  X  X  0  0  0 X^2 X^2  X X^2+X  0 X^2+X X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  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+53x^68+224x^69+203x^70+468x^71+302x^72+516x^73+285x^74+426x^75+222x^76+360x^77+204x^78+216x^79+136x^80+168x^81+65x^82+118x^83+42x^84+40x^85+8x^86+18x^87+9x^88+4x^89+2x^90+3x^92+1x^94+2x^95

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 1.07 seconds.