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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+133x^66+28x^67+303x^68+204x^69+604x^70+632x^71+733x^72+1068x^73+1070x^74+1388x^75+1327x^76+1576x^77+1251x^78+1424x^79+1119x^80+1032x^81+682x^82+564x^83+479x^84+204x^85+260x^86+56x^87+111x^88+12x^89+75x^90+4x^91+17x^92+11x^94+4x^96+7x^98+2x^100+2x^102+1x^106

The gray image is a linear code over GF(2) with n=308, k=14 and d=132.
This code was found by Heurico 1.16 in 19.1 seconds.