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  X  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  X a*X  0 a^3*X a^5*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 a^5*X a^3*X a*X  X  0
 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*X  X a^3*X  0 a*X

generates a code of length 48 over F8[X]/(X^2) who´s minimum homogenous weight is 312.

Homogenous weight enumerator: w(x)=1x^0+525x^312+756x^320+644x^328+3584x^329+518x^336+25088x^337+581x^344+483x^352+266x^360+196x^368+112x^376+14x^384

The gray image is a linear code over GF(8) with n=384, k=5 and d=312.
This code was found by Heurico 1.16 in 0.487 seconds.