The generator matrix

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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+166x^74+652x^75+1139x^76+1410x^77+2359x^78+2420x^79+3368x^80+3778x^81+4786x^82+4574x^83+5683x^84+4908x^85+5503x^86+4938x^87+4829x^88+3672x^89+3647x^90+2452x^91+1978x^92+1244x^93+894x^94+472x^95+330x^96+128x^97+109x^98+42x^99+12x^100+22x^101+8x^102+2x^103+4x^104+6x^105

The gray image is a linear code over GF(2) with n=340, k=16 and d=148.
This code was found by Heurico 1.13 in 70.9 seconds.