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

generates a code of length 51 over F8[X]/(X^2) who´s minimum homogenous weight is 328.

Homogenous weight enumerator: w(x)=1x^0+105x^328+756x^336+693x^344+3584x^350+630x^352+25088x^358+504x^360+469x^368+448x^376+203x^384+203x^392+77x^400+7x^408

The gray image is a linear code over GF(8) with n=408, k=5 and d=328.
This code was found by Heurico 1.16 in 0.518 seconds.