The generator matrix

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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+78x^64+114x^65+238x^66+314x^67+416x^68+448x^69+541x^70+718x^71+904x^72+1148x^73+1238x^74+1452x^75+1365x^76+1360x^77+1311x^78+1034x^79+886x^80+752x^81+547x^82+432x^83+319x^84+214x^85+182x^86+112x^87+93x^88+58x^89+36x^90+34x^91+32x^92+2x^93+2x^94+2x^96+1x^106

The gray image is a linear code over GF(2) with n=304, k=14 and d=128.
This code was found by Heurico 1.16 in 25.3 seconds.