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

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+62x^60+78x^61+139x^62+172x^63+277x^64+330x^65+369x^66+420x^67+576x^68+636x^69+653x^70+826x^71+649x^72+666x^73+575x^74+470x^75+342x^76+252x^77+226x^78+126x^79+110x^80+68x^81+65x^82+30x^83+26x^84+18x^85+12x^86+4x^87+3x^88+7x^90+2x^92+1x^94+1x^102

The gray image is a linear code over GF(2) with n=284, k=13 and d=120.
This code was found by Heurico 1.16 in 6.34 seconds.