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

generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+30x^62+52x^63+180x^64+228x^65+323x^66+352x^67+508x^68+618x^69+690x^70+1026x^71+1013x^72+1218x^73+1369x^74+1260x^75+1341x^76+1168x^77+1037x^78+1016x^79+759x^80+672x^81+454x^82+312x^83+226x^84+162x^85+152x^86+66x^87+51x^88+26x^89+34x^90+12x^91+13x^92+4x^93+3x^94+4x^96+3x^98+1x^106

The gray image is a linear code over GF(2) with n=300, k=14 and d=124.
This code was found by Heurico 1.16 in 24.7 seconds.