The generator matrix

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

generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+116x^65+370x^66+766x^67+820x^68+1568x^69+1605x^70+2324x^71+1818x^72+2952x^73+2740x^74+3174x^75+2115x^76+2814x^77+2370x^78+2366x^79+1277x^80+1414x^81+816x^82+644x^83+272x^84+210x^85+87x^86+62x^87+32x^88+14x^89+10x^90+8x^91+2x^94+1x^108

The gray image is a linear code over GF(2) with n=300, k=15 and d=130.
This code was found by Heurico 1.16 in 50.8 seconds.