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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+61x^74+92x^75+159x^76+266x^77+315x^78+400x^79+511x^80+594x^81+797x^82+888x^83+1000x^84+1228x^85+1301x^86+1358x^87+1325x^88+1200x^89+1012x^90+856x^91+673x^92+574x^93+447x^94+364x^95+256x^96+182x^97+189x^98+112x^99+86x^100+44x^101+33x^102+22x^103+19x^104+8x^105+4x^106+4x^107+2x^108+1x^122

The gray image is a linear code over GF(2) with n=348, k=14 and d=148.
This code was found by Heurico 1.16 in 30.3 seconds.