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

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+31x^70+54x^71+63x^72+78x^73+93x^74+136x^75+152x^76+138x^77+96x^78+54x^79+30x^80+28x^81+32x^82+12x^83+6x^84+10x^85+2x^86+4x^88+2x^89+1x^90+1x^142

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 0.369 seconds.