The generator matrix

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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+88x^65+443x^66+876x^67+1285x^68+1920x^69+2639x^70+3326x^71+4114x^72+4576x^73+4827x^74+5656x^75+5755x^76+5568x^77+5555x^78+4752x^79+4068x^80+3266x^81+2368x^82+1704x^83+1176x^84+708x^85+402x^86+246x^87+107x^88+60x^89+20x^90+12x^91+4x^92+4x^93+4x^95+2x^96+2x^97+2x^98

The gray image is a linear code over GF(2) with n=304, k=16 and d=130.
This code was found by Heurico 1.13 in 62.7 seconds.