The generator matrix

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

generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+104x^67+185x^68+462x^69+478x^70+668x^71+585x^72+816x^73+643x^74+770x^75+604x^76+684x^77+475x^78+510x^79+310x^80+292x^81+165x^82+206x^83+95x^84+46x^85+22x^86+38x^87+7x^88+4x^89+7x^90+8x^91+4x^92+1x^94+1x^96+1x^98

The gray image is a linear code over GF(2) with n=300, k=13 and d=134.
This code was found by Heurico 1.16 in 4.4 seconds.