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 X^2  0  0  0  X  X  1  X X^2  X  1  X X^2  0  X X^2  1 X^2  X  1  1  1  X  0  X  1  1  1  0  X  1  1  X  1  1
 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  0 X^2  0 X^2  0  X X^2+X  X  X X^2  0  0 X^2 X^2  0 X^2 X^2  X X^2+X  X  X X^2+X X^2  X X^2  X X^2  X  X  X  0  X  X  X X^2+X  0  0 X^2+X X^2  0 X^2 X^2
 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  0  X  0 X^2 X^2 X^2+X  0 X^2 X^2+X  0  X  X X^2+X  0  X  0  X  X  0  0 X^2+X X^2+X  X X^2  X X^2+X X^2 X^2  X  X  0  X X^2+X  X X^2 X^2 X^2 X^2 X^2 X^2 X^2  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  0  0  X X^2+X  0 X^2 X^2+X  0 X^2+X  X X^2+X  0 X^2 X^2  0  X  0 X^2 X^2+X  0  X X^2  0  X X^2 X^2+X X^2+X  0 X^2  X  X X^2  X X^2 X^2+X  X X^2 X^2+X X^2 X^2 X^2  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  X X^2+X X^2  X  X  0 X^2+X X^2+X X^2 X^2  X X^2+X X^2+X  0 X^2+X X^2+X  0  0 X^2  0 X^2 X^2+X  X  0 X^2 X^2+X X^2+X  X X^2+X  0  X  X X^2+X X^2 X^2  0 X^2+X X^2  0 X^2+X  0  0
 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  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0  0  0  0
 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  0  0 X^2  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2
 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  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  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+123x^66+453x^68+32x^69+737x^70+76x^71+951x^72+328x^73+1334x^74+580x^75+1721x^76+964x^77+1808x^78+1132x^79+1668x^80+612x^81+1339x^82+236x^83+899x^84+108x^85+605x^86+24x^87+341x^88+4x^89+164x^90+95x^92+34x^94+14x^96+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 26.6 seconds.