The generator matrix

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

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+285x^62+672x^63+949x^64+1618x^65+1782x^66+2066x^67+2134x^68+2630x^69+2680x^70+2976x^71+2959x^72+2758x^73+2293x^74+2098x^75+1644x^76+1248x^77+709x^78+628x^79+317x^80+140x^81+89x^82+50x^83+24x^84+6x^85+4x^87+4x^88+2x^90+2x^91

The gray image is a linear code over GF(2) with n=284, k=15 and d=124.
This code was found by Heurico 1.16 in 44.9 seconds.