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

generates a code of length 52 over F8[X]/(X^2) who´s minimum homogenous weight is 347.

Homogenous weight enumerator: w(x)=1x^0+3808x^347+5376x^348+168x^350+168x^351+1169x^352+5040x^353+6552x^354+17360x^355+19152x^356+896x^357+2352x^358+1008x^359+3528x^360+10080x^361+8400x^362+29120x^363+28000x^364+6272x^365+8232x^366+2408x^367+6440x^368+17136x^369+13720x^370+35728x^371+29904x^372+63x^376+21x^384+7x^392+21x^400+14x^408

The gray image is a linear code over GF(8) with n=416, k=6 and d=347.
This code was found by Heurico 1.16 in 10.2 seconds.