The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  X  X X^2 X^2+X  1 X^2  1 X^2  1  1 X^2  1 X^2  X  1  1  0 X^2+X  1  1  1 X^2 X^2 X^2  1  1  1  1  1 X^2+X  1 X^2+X  X  1  X X^2+X  1  X  1  1  X X^2 X^2+X X^2  0  1  1  X  0  0  1  1  1 X^2  0  1  1  1  1
 0  1  0  0  X  1 X^2+X+1 X^2 X^2+X X^2+1 X+1  1  1  1  X X^2  1  X  1 X+1  X X^2 X^2+X+1 X^2+X  1  X  1  1  0 X+1  X X^2+X+1  X  1  0  X X^2 X+1 X^2+X+1  0  1  1  1  0 X^2  1  X X^2+1 X^2  0 X^2+X+1 X^2+X X^2+X  X  1  1  X X^2+1 X^2  1  1 X^2+1 X^2 X^2+X+1  1  1  X X^2 X+1  0
 0  0  1  0  0  0  0  1 X^2+1  1  1 X+1  1  X  1 X^2  X X+1 X^2+X+1 X^2+X+1 X^2+1  1 X^2  0 X^2+X+1  X X+1 X^2+X  1  0 X^2+X X^2  1 X+1  X X+1  0  X X+1 X+1 X^2  0 X^2+X  1 X+1 X^2+X+1  1 X+1  X  0 X^2+X+1  1  1 X^2+X X^2+1 X^2+1 X^2+X X^2+1  1 X^2+X X+1  1 X^2+X+1  X X+1 X^2+X  1 X+1 X^2+X+1  0
 0  0  0  1  1 X^2+X+1 X^2+X X+1  0 X^2+X  1  1 X^2 X+1  1 X^2+1 X^2 X^2  X X+1  1 X+1 X^2+1  1 X+1 X^2+X  X X+1  0 X+1 X^2+X+1 X^2 X+1 X^2+1  1  1 X^2+X+1 X^2+X+1 X^2+X+1  1 X^2  0  1  0 X^2+X  X  1 X^2  1 X^2+X X^2+X+1 X^2+X+1  1  1 X^2+X+1 X^2+X X^2+1 X^2+X X^2+X+1 X^2+1  1  1  1 X^2 X+1 X^2+1 X+1 X^2+X X^2+1  0
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0
 0  0  0  0  0  0 X^2  0  0  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 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 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+97x^60+306x^61+659x^62+994x^63+1414x^64+1748x^65+1913x^66+2314x^67+2659x^68+2798x^69+2903x^70+2982x^71+2774x^72+2376x^73+1965x^74+1626x^75+1186x^76+760x^77+565x^78+376x^79+170x^80+66x^81+54x^82+28x^83+14x^84+8x^85+4x^86+5x^88+2x^89+1x^94

The gray image is a linear code over GF(2) with n=280, k=15 and d=120.
This code was found by Heurico 1.16 in 45.6 seconds.