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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+74x^65+151x^66+210x^67+331x^68+392x^69+535x^70+640x^71+757x^72+912x^73+1052x^74+1176x^75+1307x^76+1422x^77+1255x^78+1244x^79+1086x^80+840x^81+809x^82+608x^83+435x^84+370x^85+217x^86+166x^87+151x^88+70x^89+68x^90+46x^91+23x^92+16x^93+7x^94+6x^95+5x^96+2x^102

The gray image is a linear code over GF(2) with n=308, k=14 and d=130.
This code was found by Heurico 1.16 in 25.8 seconds.