The generator matrix

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

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+104x^62+44x^63+364x^64+196x^65+633x^66+416x^67+724x^68+576x^69+778x^70+616x^71+844x^72+568x^73+719x^74+416x^75+475x^76+192x^77+240x^78+44x^79+113x^80+4x^81+67x^82+30x^84+14x^86+6x^88+5x^90+3x^92

The gray image is a linear code over GF(2) with n=284, k=13 and d=124.
This code was found by Heurico 1.16 in 5.1 seconds.