The generator matrix

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

generates a code of length 51 over F8[X]/(X^2) who´s minimum homogenous weight is 344.

Homogenous weight enumerator: w(x)=1x^0+70x^344+1344x^345+560x^346+840x^347+4704x^349+217x^352+4480x^353+1120x^354+1008x^355+1344x^357+98x^360+8512x^361+1904x^362+1736x^363+4704x^365+56x^368+56x^376+14x^384

The gray image is a linear code over GF(8) with n=408, k=5 and d=344.
This code was found by Heurico 1.16 in 0.168 seconds.