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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+50x^73+108x^74+202x^75+219x^76+282x^77+330x^78+434x^79+507x^80+508x^81+582x^82+558x^83+728x^84+694x^85+580x^86+520x^87+454x^88+348x^89+212x^90+218x^91+169x^92+108x^93+82x^94+106x^95+78x^96+54x^97+18x^98+6x^99+19x^100+4x^101+8x^102+4x^103+1x^116

The gray image is a linear code over GF(2) with n=336, k=13 and d=146.
This code was found by Heurico 1.16 in 7.97 seconds.