The generator matrix

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

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+17x^62+74x^63+77x^64+102x^65+100x^66+180x^67+198x^68+200x^69+269x^70+166x^71+203x^72+136x^73+68x^74+64x^75+36x^76+58x^77+21x^78+20x^79+26x^80+14x^81+4x^82+8x^83+2x^84+2x^85+1x^86+1x^120

The gray image is a linear code over GF(2) with n=280, k=11 and d=124.
This code was found by Heurico 1.16 in 0.461 seconds.