The generator matrix

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

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+354x^61+584x^62+1052x^63+1466x^64+1722x^65+1869x^66+2262x^67+2584x^68+3012x^69+2931x^70+3034x^71+2661x^72+2596x^73+1934x^74+1596x^75+1136x^76+810x^77+455x^78+334x^79+198x^80+90x^81+31x^82+18x^83+18x^84+8x^85+4x^86+8x^87

The gray image is a linear code over GF(2) with n=280, k=15 and d=122.
This code was found by Heurico 1.13 in 15.7 seconds.