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

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+64x^65+147x^66+242x^67+259x^68+354x^69+442x^70+494x^71+715x^72+774x^73+1135x^74+1326x^75+1438x^76+1676x^77+1435x^78+1386x^79+1165x^80+820x^81+643x^82+444x^83+345x^84+290x^85+226x^86+166x^87+150x^88+102x^89+59x^90+34x^91+22x^92+16x^93+9x^94+2x^95+2x^99+1x^120

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 25.4 seconds.