The generator matrix

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

generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+454x^62+1512x^64+2314x^66+2793x^68+2636x^70+2685x^72+1982x^74+1204x^76+556x^78+177x^80+56x^82+11x^84+2x^86+1x^88

The gray image is a linear code over GF(2) with n=280, k=14 and d=124.
This code was found by Heurico 1.13 in 30.4 seconds.