The generator matrix

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

generates a code of length 73 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+82x^62+370x^63+915x^64+1340x^65+1940x^66+2506x^67+3266x^68+4074x^69+4487x^70+5032x^71+5642x^72+5762x^73+5693x^74+5728x^75+4851x^76+4014x^77+3097x^78+2352x^79+1811x^80+1084x^81+619x^82+356x^83+263x^84+94x^85+82x^86+38x^87+19x^88+14x^89+2x^91+2x^93

The gray image is a linear code over GF(2) with n=292, k=16 and d=124.
This code was found by Heurico 1.13 in 58.2 seconds.