The generator matrix

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

generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+224x^63+352x^64+666x^65+594x^66+778x^67+688x^68+754x^69+610x^70+746x^71+443x^72+576x^73+432x^74+488x^75+265x^76+232x^77+148x^78+90x^79+40x^80+40x^81+6x^82+10x^83+3x^84+2x^85+2x^86+2x^89

The gray image is a linear code over GF(2) with n=280, k=13 and d=126.
This code was found by Heurico 1.11 in 1.22 seconds.