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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+140x^70+24x^71+189x^72+48x^73+236x^74+124x^75+253x^76+132x^77+252x^78+96x^79+215x^80+72x^81+78x^82+12x^83+60x^84+4x^85+44x^86+39x^88+18x^90+10x^92+1x^124

The gray image is a linear code over GF(2) with n=308, k=11 and d=140.
This code was found by Heurico 1.16 in 4.16 seconds.