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

generates a code of length 73 over Z2[X]/(X^3) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+48x^61+154x^62+188x^63+256x^64+346x^65+439x^66+532x^67+622x^68+902x^69+1187x^70+1384x^71+1457x^72+1478x^73+1549x^74+1330x^75+1052x^76+948x^77+703x^78+460x^79+323x^80+270x^81+246x^82+168x^83+102x^84+102x^85+63x^86+32x^87+27x^88+2x^89+5x^90+2x^91+4x^94+1x^98+1x^110

The gray image is a linear code over GF(2) with n=292, k=14 and d=122.
This code was found by Heurico 1.16 in 24.5 seconds.