The generator matrix

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

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+27x^66+50x^67+105x^68+254x^69+310x^70+546x^71+513x^72+976x^73+699x^74+1508x^75+951x^76+1770x^77+1035x^78+1904x^79+924x^80+1460x^81+708x^82+902x^83+441x^84+566x^85+217x^86+190x^87+95x^88+76x^89+55x^90+20x^91+29x^92+18x^93+13x^94+9x^96+7x^98+2x^100+1x^102+2x^104

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 19.9 seconds.