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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+170x^72+506x^74+44x^75+738x^76+152x^77+1050x^78+300x^79+1247x^80+680x^81+1588x^82+876x^83+1791x^84+856x^85+1650x^86+692x^87+1296x^88+320x^89+882x^90+136x^91+596x^92+32x^93+394x^94+204x^96+8x^97+120x^98+34x^100+18x^102+2x^104+1x^116

The gray image is a linear code over GF(2) with n=336, k=14 and d=144.
This code was found by Heurico 1.16 in 30.7 seconds.