The generator matrix

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

generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+68x^61+143x^62+288x^63+222x^64+526x^65+405x^66+752x^67+508x^68+936x^69+619x^70+938x^71+456x^72+756x^73+384x^74+520x^75+172x^76+244x^77+78x^78+52x^79+32x^80+30x^81+25x^82+8x^83+8x^84+7x^86+2x^87+8x^88+2x^90+1x^94+1x^96

The gray image is a linear code over GF(2) with n=280, k=13 and d=122.
This code was found by Heurico 1.16 in 38.7 seconds.