The generator matrix

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

generates a code of length 70 over Z2[X]/(X^2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+61x^58+102x^59+220x^60+264x^61+308x^62+348x^63+366x^64+404x^65+419x^66+460x^67+471x^68+502x^69+486x^70+484x^71+441x^72+464x^73+414x^74+408x^75+319x^76+298x^77+272x^78+198x^79+174x^80+82x^81+78x^82+46x^83+50x^84+32x^85+9x^86+2x^87+6x^88+2x^89+1x^94

The gray image is a linear code over GF(2) with n=140, k=13 and d=58.
This code was found by Heurico 1.10 in 3.31 seconds.