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

generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+76x^66+146x^67+237x^68+302x^69+355x^70+504x^71+549x^72+692x^73+995x^74+1128x^75+1137x^76+1362x^77+1457x^78+1404x^79+1293x^80+1062x^81+929x^82+708x^83+532x^84+434x^85+298x^86+198x^87+172x^88+140x^89+98x^90+66x^91+40x^92+38x^93+14x^94+6x^95+4x^96+2x^97+2x^98+2x^100+1x^112

The gray image is a linear code over GF(2) with n=312, k=14 and d=132.
This code was found by Heurico 1.16 in 26.1 seconds.