The generator matrix

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

generates a code of length 52 over F8[X]/(X^2) who´s minimum homogenous weight is 336.

Homogenous weight enumerator: w(x)=1x^0+189x^336+686x^344+770x^352+3584x^357+658x^360+25088x^365+539x^368+371x^376+378x^384+252x^392+140x^400+105x^408+7x^416

The gray image is a linear code over GF(8) with n=416, k=5 and d=336.
This code was found by Heurico 1.16 in 0.529 seconds.