The generator matrix

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

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+38x^88+90x^89+307x^90+288x^91+427x^92+432x^93+658x^94+356x^95+750x^96+468x^97+836x^98+364x^99+779x^100+402x^101+639x^102+280x^103+333x^104+216x^105+193x^106+76x^107+76x^108+36x^109+32x^110+34x^111+25x^112+16x^113+17x^114+6x^115+2x^116+2x^117+2x^118+2x^119+2x^121+3x^122+2x^123+1x^126+1x^128

The gray image is a linear code over GF(2) with n=392, k=13 and d=176.
This code was found by Heurico 1.16 in 7.39 seconds.