The generator matrix

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

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+126x^66+454x^67+551x^68+1126x^69+1230x^70+1912x^71+1796x^72+2792x^73+2299x^74+2986x^75+2385x^76+3122x^77+2384x^78+2698x^79+1731x^80+1678x^81+1066x^82+1118x^83+537x^84+372x^85+169x^86+100x^87+30x^88+58x^89+21x^90+10x^91+7x^92+4x^93+2x^95+2x^96+1x^102

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 51.1 seconds.