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  1  1  1  1  1  1  1  0 X^2  X X^2  0 X^2  X  X  X  0  X  1 X^2  1  1  X X^2 X^2 X^2  X  1  X  1  1  1  X  0  0  1
 0  X  0  0  0  0  0  0  0  0 X^2  X  X X^2+X  0 X^2+X X^2+X  0 X^2  X X^2+X X^2  X  X  X X^2  X  0  X X^2 X^2+X  X X^2+X X^2+X X^2+X X^2+X  X X^2  0 X^2+X X^2+X X^2  X X^2+X  X  0 X^2  X X^2+X  0  X  0 X^2  X  X  0 X^2  0  X X^2+X X^2+X X^2+X  X X^2  0  0  X X^2 X^2  X X^2  0  0  X  0
 0  0  X  0  0  0  0  0  0  0 X^2+X X^2  X  X  X  X  0  X  X  0 X^2+X X^2  0 X^2+X  X  X X^2+X X^2+X X^2  0 X^2+X  0 X^2 X^2+X  X  0 X^2 X^2  X  0 X^2  X X^2+X X^2+X  X  X  0 X^2 X^2 X^2 X^2+X  X  X X^2+X  0  X X^2+X  0  0 X^2+X X^2+X X^2 X^2  X  X  X  0  X  X  0  X X^2  X  0  0
 0  0  0  X  0  0  0  X X^2+X  X  X X^2+X  0  X X^2  0 X^2+X X^2+X X^2 X^2+X X^2+X  X  0 X^2  0 X^2  X  X  X X^2  X  0 X^2+X  0  X X^2+X  0 X^2  X  X X^2 X^2+X  0 X^2  X  0  0  0  0 X^2  X  0  X  0  0 X^2 X^2 X^2+X X^2+X X^2 X^2+X X^2+X X^2+X X^2+X  X X^2+X  0 X^2+X  0 X^2+X  X X^2  0 X^2+X X^2+X
 0  0  0  0  X  0  X  X  X X^2  X  X  X X^2 X^2 X^2+X X^2+X X^2 X^2+X X^2 X^2+X  X X^2+X X^2 X^2  X  0 X^2+X X^2 X^2+X X^2+X  X X^2+X  X  0 X^2+X X^2+X  0  0 X^2  X X^2  0 X^2+X X^2 X^2  X  X  X  X  X  X X^2 X^2+X  0  0  X X^2  0  0  0 X^2+X  X  0  0  X  X X^2+X X^2+X  0 X^2+X X^2+X X^2  0  0
 0  0  0  0  0  X  X X^2 X^2+X X^2+X  X  X X^2+X  0  X X^2 X^2 X^2  X X^2+X  0 X^2 X^2  0  X  0  X X^2 X^2 X^2+X X^2+X X^2+X X^2+X  0 X^2 X^2 X^2 X^2  0  0 X^2+X X^2+X X^2+X X^2+X  X  X X^2 X^2 X^2+X X^2+X X^2+X  0  X X^2 X^2 X^2 X^2  X X^2 X^2 X^2+X  X X^2  0 X^2+X  0  X X^2  0  X  X X^2+X X^2 X^2+X  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  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+56x^63+140x^64+214x^65+288x^66+376x^67+472x^68+582x^69+725x^70+798x^71+1122x^72+1362x^73+1418x^74+1482x^75+1362x^76+1272x^77+1101x^78+922x^79+708x^80+510x^81+397x^82+310x^83+221x^84+182x^85+128x^86+80x^87+65x^88+34x^89+37x^90+8x^91+4x^92+4x^93+2x^94+1x^108

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 25.7 seconds.