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

generates a code of length 94 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+48x^84+114x^85+215x^86+310x^87+385x^88+460x^89+549x^90+590x^91+608x^92+696x^93+628x^94+610x^95+572x^96+492x^97+488x^98+376x^99+319x^100+218x^101+123x^102+128x^103+83x^104+54x^105+20x^106+24x^107+19x^108+10x^109+21x^110+8x^111+8x^112+2x^113+3x^114+2x^115+2x^116+2x^117+1x^118+3x^120

The gray image is a linear code over GF(2) with n=376, k=13 and d=168.
This code was found by Heurico 1.16 in 6.62 seconds.