The generator matrix

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

generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+372x^88+548x^89+1082x^90+1296x^91+1660x^92+1652x^93+1978x^94+1968x^95+2420x^96+2328x^97+2648x^98+2352x^99+2376x^100+1924x^101+1946x^102+1556x^103+1380x^104+940x^105+882x^106+488x^107+434x^108+208x^109+146x^110+84x^111+59x^112+16x^113+20x^114+2x^116+2x^118

The gray image is a linear code over GF(2) with n=392, k=15 and d=176.
This code was found by Heurico 1.13 in 25 seconds.