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

generates a code of length 73 over Z2[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+63x^60+40x^61+170x^62+180x^63+277x^64+348x^65+524x^66+580x^67+671x^68+972x^69+1013x^70+1272x^71+1376x^72+1402x^73+1381x^74+1360x^75+1084x^76+900x^77+707x^78+568x^79+433x^80+356x^81+216x^82+120x^83+147x^84+72x^85+67x^86+12x^87+31x^88+6x^89+13x^90+4x^91+11x^92+3x^94+1x^96+2x^98+1x^104

The gray image is a linear code over GF(2) with n=292, k=14 and d=120.
This code was found by Heurico 1.16 in 23.7 seconds.