The generator matrix

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

generates a code of length 99 over Z2[X]/(X^3) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+48x^89+138x^90+258x^91+239x^92+474x^93+380x^94+652x^95+405x^96+810x^97+413x^98+780x^99+466x^100+752x^101+362x^102+600x^103+322x^104+390x^105+162x^106+224x^107+67x^108+60x^109+48x^110+34x^111+21x^112+24x^113+23x^114+10x^115+11x^116+2x^117+8x^118+2x^119+2x^120+2x^126+1x^128+1x^132

The gray image is a linear code over GF(2) with n=396, k=13 and d=178.
This code was found by Heurico 1.16 in 38.1 seconds.