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

generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+68x^85+160x^86+202x^87+295x^88+356x^89+482x^90+482x^91+608x^92+758x^93+934x^94+1042x^95+1071x^96+1266x^97+1206x^98+1240x^99+1064x^100+1022x^101+908x^102+704x^103+583x^104+392x^105+358x^106+298x^107+244x^108+178x^109+142x^110+98x^111+80x^112+50x^113+34x^114+28x^115+20x^116+6x^117+2x^119+1x^120+1x^136

The gray image is a linear code over GF(2) with n=392, k=14 and d=170.
This code was found by Heurico 1.16 in 36 seconds.