The generator matrix

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

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+74x^66+460x^67+886x^68+1368x^69+1966x^70+2692x^71+3077x^72+4260x^73+4393x^74+5252x^75+5352x^76+5798x^77+5707x^78+5324x^79+4389x^80+4294x^81+3206x^82+2528x^83+1680x^84+1198x^85+728x^86+452x^87+215x^88+122x^89+51x^90+24x^91+14x^92+12x^93+3x^94+4x^95+2x^96+4x^97

The gray image is a linear code over GF(2) with n=308, k=16 and d=132.
This code was found by Heurico 1.13 in 63 seconds.