The generator matrix

 1  0  0  0  1  1  1  X  1  1 X^2+X  1  1  X X^2  1 X^2  1  1  1  0  X  X X^2+X  1  0  1  1  1  0  1 X^2  0  1  1  1 X^2+X  1  1  1  1 X^2 X^2+X X^2  1  1  X X^2+X  1  1 X^2  X  1  0  1  X  1  X X^2+X  1  1  1  0  1  0 X^2+X  1  1  1  1  0  1  1  X X^2+X X^2+X  0 X^2  X X^2  1  1  0  1  1 X^2+X  1 X^2+X  1 X^2  0  1  X  1  X  1  1  1
 0  1  0  0  X  1 X^2+X+1  1 X+1 X^2  1  X X^2+1  1  0 X^2  1  X X^2+X X^2+1  0  1  1 X^2 X+1  X  1  X  0  1  0  1  1 X+1  0 X^2+X  1 X^2+X X^2+X+1 X^2+X+1 X+1  X  0  1  0  1  1 X^2+X X+1 X+1 X^2+X X^2  1  1 X^2+X+1  1 X^2  1  1  0  X X^2+X+1  1  0  1 X^2 X^2  0  X X^2+X  1 X^2+X+1  0  1  X  0  1 X^2+X X^2  1 X^2+X+1 X^2+1  0  1  X X^2 X^2+X+1  0 X^2+X  0  1 X+1  1 X^2+X+1 X^2+X X+1  0 X^2
 0  0  1  0  0  0  0 X^2 X^2+1 X^2+1  1  1 X^2+X+1 X^2+X+1  1 X^2+X X^2+X X+1 X^2+X+1  0  X X^2 X^2+X+1  1  X  1 X+1 X^2+X  X X^2+1 X+1  0 X^2+1 X+1 X+1 X+1  1  X X^2+1  1 X^2 X^2  1 X^2 X^2+1  X X^2+X  1 X^2+X  1  1  X  1 X+1  X X^2+1  X X^2+X+1 X^2+X X^2+1 X^2+X X+1  1  1 X^2+X  0  X X+1  X X+1 X^2  0  0 X^2+X X^2 X^2+X X^2  X  1  X X^2+X+1  0  1  0  0  0 X+1  1  1  1 X^2+1 X+1  1 X+1  1 X^2 X^2+1  0
 0  0  0  1  1 X^2+X+1 X^2+X X^2+1 X+1  1 X^2  0  X X+1 X^2+X+1 X+1  0  1  X X^2  1 X+1 X^2+X+1 X^2+1 X+1  X  0  1 X^2  0 X^2+X  X X+1 X+1 X^2+1  1 X^2+X X^2+X X^2 X^2+1 X^2  1 X^2+X+1  1 X^2+X+1 X+1 X^2+X+1  1 X^2+X X^2 X^2  1 X^2+X+1  1  X X^2+X X^2+X+1 X^2+X X^2  1 X^2+X+1 X+1  1  X X^2+X+1  1 X^2+X+1 X+1 X^2 X^2  X X^2+X+1 X^2  X  1  1 X^2+X  1 X^2+X+1 X^2 X+1 X^2  X  0 X^2  1  X  X X^2+X  X X+1 X^2+X  1  1  0  X  1 X^2+X
 0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2
 0  0  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 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  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+70x^87+427x^88+510x^89+1039x^90+1144x^91+1575x^92+1610x^93+2178x^94+1916x^95+2722x^96+2068x^97+2712x^98+2052x^99+2692x^100+1854x^101+2241x^102+1392x^103+1343x^104+906x^105+905x^106+524x^107+395x^108+184x^109+124x^110+56x^111+51x^112+26x^113+14x^114+8x^115+8x^116+8x^117+1x^118+6x^119+2x^121+2x^122+2x^124

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 70.3 seconds.