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

generates a code of length 47 over F8[X]/(X^2) who´s minimum homogenous weight is 304.

Homogenous weight enumerator: w(x)=1x^0+392x^304+777x^312+630x^320+679x^328+28672x^329+518x^336+399x^344+315x^352+301x^360+56x^368+28x^376

The gray image is a linear code over GF(8) with n=376, k=5 and d=304.
This code was found by Heurico 1.16 in 0.463 seconds.