The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  0  1  1 X^2+X  1  1  X  1  1  0  1  1  1 X^2  1 X^2+X  1  1  1  1  0  1  1 X^2+X  1  0  1  1 X^2+X  1  1  0 X^2+X  1 X^2+X  1  0  0  1  1  1 X^2 X^2+X  1  1  X  1  1  1  0  1 X^2+X  1  1  1  1 X^2+X  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  1  0 X^2+1  1 X^2+X X+1  1 X^2+X+1  0  1 X^2+X X^2+1 X^2+1  1  0  1 X^2+X X+1 X^2 X^2+X  1 X^2+1  0  1 X+1  1 X^2+X X+1  1  0 X^2+1  1  1 X^2+1  1 X+1  1  1  1  0 X^2+X  1  1 X^2 X+1  1 X^2+X X^2 X+1  1 X^2+1  1 X^2+X+1  0 X^2+1 X+1  1  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2  0  0  0 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2 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 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0  0  0 X^2  0  0
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0
 0  0  0  0  0  0  0 X^2  0 X^2  0  0  0  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  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0  0  0  0  0 X^2  0 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 60.

Homogenous weight enumerator: w(x)=1x^0+52x^60+68x^61+118x^62+232x^63+238x^64+508x^65+387x^66+692x^67+528x^68+1060x^69+516x^70+1060x^71+495x^72+692x^73+361x^74+508x^75+186x^76+232x^77+110x^78+68x^79+22x^80+22x^82+8x^84+12x^86+3x^88+5x^90+2x^92+4x^94+1x^96+1x^98

The gray image is a linear code over GF(2) with n=280, k=13 and d=120.
This code was found by Heurico 1.16 in 4.69 seconds.