The generator matrix

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

generates a code of length 53 over F8[X]/(X^2) who´s minimum homogenous weight is 344.

Homogenous weight enumerator: w(x)=1x^0+224x^344+112x^346+504x^348+224x^351+3024x^352+1064x^353+3304x^354+2408x^356+2016x^359+12068x^360+3528x^361+8232x^362+5880x^364+9632x^367+42966x^368+11256x^369+23352x^370+11256x^372+16800x^375+59234x^376+12824x^377+22344x^378+8624x^380+455x^384+357x^392+210x^400+168x^408+56x^416+21x^424

The gray image is a linear code over GF(8) with n=424, k=6 and d=344.
This code was found by Heurico 1.16 in 12.6 seconds.