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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+48x^64+74x^65+160x^66+186x^67+281x^68+398x^69+466x^70+610x^71+765x^72+932x^73+1107x^74+1148x^75+1330x^76+1374x^77+1324x^78+1368x^79+1095x^80+920x^81+713x^82+598x^83+381x^84+310x^85+218x^86+150x^87+135x^88+72x^89+90x^90+36x^91+48x^92+14x^93+16x^94+12x^96+2x^97+1x^98+1x^106

The gray image is a linear code over GF(2) with n=308, k=14 and d=128.
This code was found by Heurico 1.16 in 25.7 seconds.