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  0  X  1  0  1  X  1  X X^2  1  1  1  1  1  1  1  X  1  0 X^2  X  1  0  1  1  1  X  1  X  1  1  0  X X^2  0 X^2  0  0  1  0  1  1
 0  X  0  X  0  0  X X^2+X  0 X^2 X^2+X  X  0  X  X X^2 X^2 X^2+X  0  X X^2+X  0  X X^2  X  X X^2 X^2+X  X X^2+X  0  X X^2 X^2  0  0  X  0  X X^2 X^2  X X^2 X^2 X^2+X X^2+X  0  X  X X^2+X X^2  X X^2+X  X  0  X X^2+X X^2+X  X  X X^2+X  X  X  0 X^2  0  0  X  0  0
 0  0  X  X  0 X^2+X  X  0 X^2  X  0  X  0 X^2+X X^2  X  X X^2  0 X^2+X X^2+X  X X^2  0 X^2  X  X X^2+X  0 X^2 X^2  0  0  X X^2 X^2+X  X X^2+X  0 X^2+X X^2+X  X  0 X^2  0 X^2+X  X X^2+X  X  0  X X^2  0 X^2+X X^2+X  0  X X^2+X X^2 X^2  0  X X^2  X  X  X  X  0  0  0
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 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 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  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 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 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  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0  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+42x^60+26x^61+104x^62+148x^63+187x^64+238x^65+229x^66+292x^67+319x^68+344x^69+350x^70+364x^71+308x^72+292x^73+216x^74+148x^75+116x^76+90x^77+80x^78+64x^79+40x^80+30x^81+30x^82+8x^83+11x^84+4x^85+10x^86+4x^90+1x^98

The gray image is a linear code over GF(2) with n=280, k=12 and d=120.
This code was found by Heurico 1.16 in 1.54 seconds.