The generator matrix

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

generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+323x^64+740x^66+917x^68+616x^70+536x^72+444x^74+260x^76+160x^78+58x^80+24x^82+15x^84+2x^88

The gray image is a linear code over GF(2) with n=280, k=12 and d=128.
This code was found by Heurico 1.16 in 2.35 seconds.