The generator matrix

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

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+236x^64+228x^65+470x^66+296x^67+498x^68+336x^69+408x^70+236x^71+345x^72+204x^73+248x^74+128x^75+189x^76+56x^77+106x^78+44x^79+29x^80+8x^81+14x^82+12x^84+2x^86+1x^88+1x^92

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 1.55 seconds.