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  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  X  1  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 X+a^3 a^2*X+a^3 a^6*X+1  1 a^6*X+a^6 a*X+a^5 a^4*X+a^5 a^5*X+a^2 a*X+a  1 a*X+a^3 a^4*X+1  0 a*X+1 a^5*X+a^2  X a^5*X+a^4 a^2 a^5*X+a^4 a*X+a  1 a^5*X+a^2 X+a^4 a*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^3*X a^4*X a^2*X a^4*X  X a^2*X  0 a*X a^2*X a^3*X a^4*X  X a^2*X a^6*X a^4*X  0 a*X a^4*X  X a^4*X a^3*X a^6*X a^3*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  X a^2*X a^3*X  0 a^6*X a^4*X a^6*X a^2*X a^6*X  X a^5*X  X a^3*X a^5*X a^3*X a*X a^3*X a^2*X a^4*X a^5*X a^6*X a^6*X a*X  0 a*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+147x^328+168x^331+56x^332+742x^336+504x^338+6160x^339+1624x^340+1869x^344+2968x^346+20832x^347+4200x^348+8897x^352+10472x^354+68208x^355+11592x^356+19754x^360+14728x^362+76664x^363+11200x^364+413x^368+336x^376+378x^384+175x^392+49x^400+7x^408

The gray image is a linear code over GF(8) with n=408, k=6 and d=328.
This code was found by Heurico 1.16 in 12.2 seconds.