The generator matrix

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

generates a code of length 92 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+48x^84+70x^85+90x^86+128x^87+141x^88+146x^89+170x^90+196x^91+201x^92+194x^93+144x^94+132x^95+81x^96+70x^97+68x^98+32x^99+26x^100+24x^101+28x^102+20x^103+9x^104+8x^105+9x^106+4x^107+5x^108+2x^110+1x^154

The gray image is a linear code over GF(2) with n=368, k=11 and d=168.
This code was found by Heurico 1.16 in 1.03 seconds.