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

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+180x^70+8x^71+93x^72+140x^73+199x^74+168x^75+54x^76+396x^77+164x^78+184x^79+72x^80+100x^81+118x^82+24x^83+16x^84+4x^85+76x^86+17x^88+27x^90+2x^92+4x^94+1x^128

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 36.8 seconds.