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

generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+77x^70+4x^71+159x^72+20x^73+182x^74+116x^75+237x^76+132x^77+302x^78+108x^79+235x^80+92x^81+124x^82+28x^83+88x^84+12x^85+57x^86+35x^88+22x^90+11x^92+4x^94+1x^96+1x^128

The gray image is a linear code over GF(2) with n=312, k=11 and d=140.
This code was found by Heurico 1.16 in 0.696 seconds.