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

generates a code of length 51 over F8[X]/(X^2) who´s minimum homogenous weight is 312.

Homogenous weight enumerator: w(x)=1x^0+238x^312+1232x^320+2156x^328+3535x^336+13167x^344+70322x^352+159012x^360+4851x^368+3941x^376+2499x^384+994x^392+168x^400+28x^408

The gray image is a linear code over GF(8) with n=408, k=6 and d=312.
This code was found by Heurico 1.16 in 30.8 seconds.