The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+213x^88+276x^89+556x^90+508x^91+636x^92+552x^93+740x^94+588x^95+682x^96+516x^97+552x^98+416x^99+486x^100+360x^101+332x^102+188x^103+198x^104+112x^105+120x^106+48x^107+41x^108+8x^109+22x^110+8x^111+10x^112+8x^114+4x^115+5x^116+6x^118

The gray image is a linear code over GF(2) with n=384, k=13 and d=176.
This code was found by Heurico 1.16 in 10 seconds.