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

generates a code of length 53 over F8[X]/(X^2) who´s minimum homogenous weight is 354.

Homogenous weight enumerator: w(x)=1x^0+3080x^354+5992x^355+112x^357+840x^358+672x^359+6923x^360+2520x^361+15512x^362+25928x^363+1568x^365+5040x^366+2240x^367+13580x^368+3024x^369+22456x^370+34104x^371+5488x^373+12040x^374+4256x^375+22869x^376+5208x^377+30632x^378+37912x^379+84x^384+14x^392+35x^400+14x^408

The gray image is a linear code over GF(8) with n=424, k=6 and d=354.
This code was found by Heurico 1.16 in 10.1 seconds.