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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+66x^72+100x^73+160x^74+242x^75+336x^76+358x^77+500x^78+648x^79+757x^80+912x^81+1074x^82+1272x^83+1202x^84+1354x^85+1342x^86+1114x^87+1009x^88+856x^89+718x^90+600x^91+403x^92+340x^93+323x^94+214x^95+161x^96+92x^97+91x^98+62x^99+31x^100+18x^101+14x^102+8x^103+2x^104+1x^106+2x^109+1x^118

The gray image is a linear code over GF(2) with n=340, k=14 and d=144.
This code was found by Heurico 1.16 in 30.7 seconds.