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  X  0  1  1  X  0  1  1  X  1  1  1  1  0  1  1  X  1  0  1  1  X  1  1  0  1  1  0  X  1  X  0  1  0  1  1  1  1  1 X^2  1  X  X
 0  X  0 X^2+X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X  0 X^2+X  X  0 X^2 X^2 X^2+X X^2+X  0  0 X^2+X  X X^2  0 X^2 X^2+X  X X^2+X  X X^2+X  X  X  0 X^2+X X^2+X X^2  0 X^2+X  X X^2+X  X X^2+X  0  X  X X^2+X X^2+X  X X^2  X  0  0  X X^2+X  0 X^2+X  X X^2  X X^2+X  X X^2 X^2 X^2+X  0  X X^2+X  0
 0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 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 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0
 0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0  0  0 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0
 0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0  0 X^2  0  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  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0  0 X^2  0
 0  0  0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  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+96x^60+4x^61+140x^62+48x^63+220x^64+168x^65+238x^66+328x^67+221x^68+464x^69+279x^70+488x^71+213x^72+344x^73+221x^74+152x^75+190x^76+44x^77+101x^78+8x^79+62x^80+28x^82+13x^84+13x^86+6x^88+1x^90+3x^94+1x^96+1x^104

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 1.74 seconds.