The generator matrix

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X 0 0 X 0 X 0 X X 0 X X 1 1 0 0 1 0 1 X 1 0 1 0 X X 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 X X 1 X 1 0 X 1 1 X 1
X 1 1 X 1 X+1 X 0 0 X+1 X 1 X 1 X 1 X 1 0 1 0 1 X 1 1 0 1 X 1 X+1 1 X 1 0 0 X 0 X+1 1 X 1 0 X 1 1 X+1 X 1 X 0 1 0 X+1 X X+1 X+1 X X X+1 1 1 0 X 0 X 1 0 X X 0
1 0 1 0 X+1 0 X X+1 0 X+1 1 X X+1 X+1 X 0 0 0 1 0 X 1 X 1 X X 1 1 X 0 1 1 X+1 0 1 X+1 1 0 1 X+1 X 1 0 X 1 0 0 1 1 X X X X+1 X X X+1 1 X 1 X+1 1 X X 0 1 X+1 0 X+1 0 0
0 0 0 X X+1 1 1 1 X X 1 X+1 0 1 1 X X X X+1 1 0 X+1 1 X 0 1 X+1 X 1 0 X 0 0 1 X+1 1 1 X+1 X+1 X+1 1 0 1 X+1 X+1 X 0 X 0 1 X X 1 X X+1 1 X 0 0 0 0 1 1 X+1 X+1 X 1 1 1 0
0 0 0 X X+1 1 X+1 X+1 X+1 X+1 0 X X+1 0 0 X+1 0 X+1 X X+1 1 X+1 X+1 0 X 0 X X X 0 0 1 1 X+1 X+1 1 X X+1 0 X 1 X 0 0 X+1 X X X+1 1 0 X+1 X+1 X X 1 0 X+1 X X 0 1 1 1 0 X 0 X+1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 X X X 0 0 1 X+1 1 1 1 X+1 X+1 X+1 1 1 X+1 1 1 X 0 X+1 X+1 X X+1 1 0 1 X 1 X 0 X 1 0 1 X X+1 0 X+1 X+1 1 1 1 X 1 0 1 0 X 0 1 X X+1 X+1 0 0 0 X+1 1
0 0 0 X X+1 1 X+1 X+1 X+1 X+1 0 X 1 X X 1 0 1 X X+1 1 1 1 X X X X X 0 X X 1 X+1 X+1 1 0 X+1 0 1 X+1 0 X+1 X+1 1 0 X+1 1 X X X+1 X 0 1 X+1 0 X+1 1 X+1 1 1 0 1 0 0 1 0 0 1 0 1

generates a code of length 70 over Z2[X]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+74x^57+165x^58+274x^59+363x^60+440x^61+579x^62+590x^63+691x^64+810x^65+893x^66+926x^67+900x^68+968x^69+1004x^70+1036x^71+922x^72+918x^73+910x^74+768x^75+729x^76+646x^77+497x^78+408x^79+318x^80+204x^81+167x^82+88x^83+40x^84+34x^85+8x^86+6x^87+4x^88+2x^89+1x^122

The gray image is a linear code over GF(2) with n=140, k=14 and d=57.
This code was found by an older version of Heurico in 0 seconds.