The generator matrix

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

generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+64x^63+130x^64+202x^65+296x^66+356x^67+461x^68+584x^69+635x^70+932x^71+1099x^72+1254x^73+1478x^74+1452x^75+1501x^76+1268x^77+1145x^78+942x^79+635x^80+560x^81+378x^82+258x^83+211x^84+170x^85+147x^86+86x^87+53x^88+56x^89+16x^90+6x^91+1x^92+2x^93+1x^94+1x^96+2x^100+1x^112

The gray image is a linear code over GF(2) with n=300, k=14 and d=126.
This code was found by Heurico 1.16 in 25.8 seconds.