The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1 X^2+X X^2+X  X  X  1  1  X X^2  1 X^2  1  1  1  1 X^2  1  0  0  1  X  1  1  1  X X^2+X  X  1  X  1  0 X^2+X X^2  1  X X^2  X  1  1  1 X^2+X  1 X^2+X  1  1  1  X  1 X^2+X  1  1  1  1  0  1  0  1 X^2+X  1  1  1  1  1  X
 0  1  0  0  1 X^2  1  1 X^2+1  0 X^2+X+1  X  1 X^2+X  1  1 X^2 X^2+X+1  0  1  0  X  0  X X+1 X^2+1 X^2 X+1  1  1 X^2+X X^2  0  1  X  1  1  1 X^2+X+1  1 X+1 X^2 X^2  1 X^2+1 X^2+X  1 X^2+X X^2+X+1  1  X X^2+X  0  1  0 X+1 X^2+1  1  1  1 X+1  X  1 X^2+1  1 X^2  1 X+1  1 X^2+1  0 X^2+X+1  1 X^2+X  0
 0  0  1  0  X  0 X^2+X  X  1  1 X+1 X^2+X+1  1  1 X^2+X  1 X^2  1  1 X^2+X+1 X^2+X X^2+X X^2+X+1 X^2+X+1 X^2+X  0  1 X^2+1 X^2  1  1 X^2+X X^2  0 X^2 X+1  1  0 X^2+X+1 X^2  X  1  1 X^2+X X^2+X  1  0  1 X^2+X X^2+X+1 X^2+X  1  X X^2 X^2+1 X^2 X^2  X  0 X^2+X+1 X^2+1  X  X  1 X^2+X+1 X^2  1  1 X^2+1 X^2+X  X X+1 X^2+X X^2+1 X^2+X
 0  0  0  1  X  1 X+1 X+1 X+1  X  0  1 X+1 X^2+X+1  X X^2+X  X X^2+1 X^2+X X+1  1  1 X^2+X X^2+X+1 X^2+X+1  0  1 X^2+X X^2+X+1 X^2+X X^2+X+1  1 X^2+X+1 X^2+1 X^2+1 X^2+X+1 X^2  X X^2+1 X+1 X^2 X+1 X^2+X  X X^2+X  0 X^2+X  X X^2+X  0  X  1  X X+1  0 X+1 X^2+X X^2+1 X^2+X X^2+X  X X^2 X^2+X+1 X^2 X^2+X+1 X^2 X^2+1  0  1  1  1 X^2+X+1 X^2 X+1  1
 0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 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+264x^68+464x^69+614x^70+576x^71+727x^72+664x^73+754x^74+616x^75+600x^76+596x^77+530x^78+460x^79+455x^80+244x^81+236x^82+160x^83+82x^84+44x^85+54x^86+12x^87+29x^88+4x^89+2x^90+2x^92+2x^94

The gray image is a linear code over GF(2) with n=300, k=13 and d=136.
This code was found by Heurico 1.11 in 2.01 seconds.