The generator matrix

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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+116x^66+404x^67+623x^68+1238x^69+1271x^70+1826x^71+1871x^72+2422x^73+2388x^74+2822x^75+2711x^76+2960x^77+2621x^78+2474x^79+1898x^80+1692x^81+1173x^82+986x^83+452x^84+402x^85+154x^86+116x^87+54x^88+54x^89+15x^90+12x^91+2x^92+6x^94+4x^96

The gray image is a linear code over GF(2) with n=304, k=15 and d=132.
This code was found by Heurico 1.16 in 50.5 seconds.