The generator matrix

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

generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+78x^58+386x^59+838x^60+1512x^61+2384x^62+3544x^63+4660x^64+6306x^65+7363x^66+9760x^67+10215x^68+12310x^69+11761x^70+12118x^71+10943x^72+10010x^73+7755x^74+6544x^75+4567x^76+3292x^77+2017x^78+1204x^79+636x^80+442x^81+184x^82+100x^83+62x^84+46x^85+10x^86+6x^87+12x^88+2x^89+2x^91+2x^92

The gray image is a linear code over GF(2) with n=280, k=17 and d=116.
This code was found by Heurico 1.13 in 218 seconds.