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  1  1  X  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  1 X^2+X+1  1 X^2+X X^2
 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  X  0 X+1 X^2+X  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 X^2+X+1  1  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^2+X+1 X^2  0  X 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+250x^61+698x^62+1092x^63+1514x^64+1536x^65+2114x^66+2210x^67+2475x^68+2860x^69+3224x^70+2768x^71+2738x^72+2498x^73+2107x^74+1498x^75+1309x^76+718x^77+478x^78+330x^79+171x^80+82x^81+49x^82+20x^83+14x^84+8x^85+2x^86+2x^87+2x^88

The gray image is a linear code over GF(2) with n=280, k=15 and d=122.
This code was found by Heurico 1.16 in 46.8 seconds.