The generator matrix

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

generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+102x^87+309x^88+728x^89+886x^90+1396x^91+1310x^92+1780x^93+1804x^94+2254x^95+2180x^96+2578x^97+2486x^98+2456x^99+2185x^100+2310x^101+1876x^102+1702x^103+1209x^104+1160x^105+604x^106+580x^107+298x^108+236x^109+138x^110+66x^111+53x^112+30x^113+8x^114+16x^115+7x^116+10x^117+6x^118+4x^119

The gray image is a linear code over GF(2) with n=392, k=15 and d=174.
This code was found by Heurico 1.16 in 69.8 seconds.