The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1 a^6*X  1  1  1  1  1  1  1  1  1  1  1 a^2*X  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1 a^5*X  1  1  1 a^6*X  1  1  1 a^6*X  1
 0  1  0  1  a a^2 a^6*X+a^3 a^6*X+a^4 a^5 a^6 a^6*X a^6*X+1 X+a X+a^2  1 a^6*X+a^5  X a^5*X+1 a^5*X+a^3 a^6*X+a^2 a^4 a^6*X+a^6 a^4*X+a a*X+a^3 a^5*X+a^6 X+a^5  1 a^4 X+a^4 a^2*X+1 a^4*X+a^3 a*X+a^6 a^4*X a^3*X+a^2 a*X+a^5 a^3*X X+a^4  1 a^4*X+a^2 a^6*X+a a^5*X+a^5 a*X+a^4 a^6*X+a a^5 a*X  1 a^3*X+a^2 a*X+a a*X  1 X+1 a^3*X+a^3 a^4*X+a^6 a^5*X a^3*X+1
 0  0  1 a^6  a a^4  1 a^5 a^3 a^2 a^3*X+1 a*X+a^5 a^6*X a^5*X+a^2 X+a^6 X+1 a^5*X+a^3 a^6*X+a a^5*X+a^6 a^5*X a^6*X+a^6 a^2*X+a^5 a^2*X+a^4 X+a a^4*X+a^3 a^3*X+a^2 a^4*X+a a^5*X+a^4 a^2*X+a^3 a^2*X+a^2 X+a^4 a^4*X a^3*X+a^6 a^3*X+1 a^4*X+a X+1 a^3*X a^6*X+a^4 a^5*X+a^5 a^2*X+a^6 a^4*X+1 a*X+a^6 a^3*X+a^5 a^3*X+a^4 a*X+a^4 X+a^6 X+a^6 X+a^3 a^5*X+a  X a^6*X+a^3 a^5*X+1 a^2*X+a^5  1 a^6*X+a^4

generates a code of length 55 over F8[X]/(X^2) who´s minimum homogenous weight is 368.

Homogenous weight enumerator: w(x)=1x^0+2737x^368+6160x^369+2128x^370+56x^371+672x^372+1344x^373+2240x^374+7392x^375+12950x^376+22008x^377+7336x^378+784x^379+4032x^380+4480x^381+4480x^382+9408x^383+19831x^384+30688x^385+11200x^386+2744x^387+9632x^388+8512x^389+7616x^390+15456x^391+25823x^392+34328x^393+8008x^394+28x^400+28x^408+28x^416+7x^424+7x^432

The gray image is a linear code over GF(8) with n=440, k=6 and d=368.
This code was found by Heurico 1.16 in 10.6 seconds.