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

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+42x^74+116x^75+147x^76+218x^77+285x^78+338x^79+411x^80+552x^81+541x^82+550x^83+667x^84+700x^85+676x^86+582x^87+542x^88+398x^89+326x^90+256x^91+191x^92+166x^93+123x^94+102x^95+68x^96+56x^97+51x^98+38x^99+17x^100+20x^101+4x^102+2x^103+2x^104+2x^105+1x^108+1x^124

The gray image is a linear code over GF(2) with n=340, k=13 and d=148.
This code was found by Heurico 1.16 in 7.88 seconds.