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

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+188x^72+452x^74+32x^75+815x^76+92x^77+1008x^78+340x^79+1340x^80+668x^81+1568x^82+900x^83+1735x^84+964x^85+1546x^86+636x^87+1313x^88+308x^89+946x^90+140x^91+587x^92+16x^93+384x^94+241x^96+104x^98+46x^100+6x^102+5x^104+2x^106+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 29.7 seconds.