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

generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+60x^58+102x^59+187x^60+270x^61+322x^62+484x^63+610x^64+710x^65+967x^66+1098x^67+1245x^68+1510x^69+1398x^70+1326x^71+1375x^72+1196x^73+933x^74+716x^75+481x^76+400x^77+323x^78+194x^79+160x^80+116x^81+83x^82+44x^83+34x^84+20x^85+9x^86+4x^87+2x^88+2x^89+1x^92+1x^98

The gray image is a linear code over GF(2) with n=280, k=14 and d=116.
This code was found by Heurico 1.16 in 23.5 seconds.