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

generates a code of length 49 over F8[X]/(X^2) who´s minimum homogenous weight is 304.

Homogenous weight enumerator: w(x)=1x^0+952x^304+1988x^312+2947x^320+3416x^328+3584x^329+4284x^336+50176x^337+5222x^344+175616x^345+5355x^352+4333x^360+2758x^368+1260x^376+231x^384+21x^392

The gray image is a linear code over GF(8) with n=392, k=6 and d=304.
This code was found by Heurico 1.16 in 54.1 seconds.