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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+57x^70+4x^71+121x^72+36x^73+93x^74+88x^75+247x^76+88x^77+113x^78+36x^79+53x^80+4x^81+51x^82+20x^84+6x^86+5x^88+1x^140

The gray image is a linear code over GF(2) with n=304, k=10 and d=140.
This code was found by Heurico 1.16 in 0.374 seconds.