The generator matrix

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

generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+44x^59+118x^60+170x^61+261x^62+398x^63+591x^64+638x^65+1013x^66+1304x^67+1314x^68+1600x^69+1573x^70+1498x^71+1506x^72+1248x^73+936x^74+704x^75+470x^76+382x^77+248x^78+134x^79+72x^80+50x^81+43x^82+12x^83+18x^84+8x^85+13x^86+2x^87+6x^88+6x^90+1x^94+2x^98

The gray image is a linear code over GF(2) with n=280, k=14 and d=118.
This code was found by Heurico 1.16 in 23.2 seconds.