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

generates a code of length 49 over F8[X]/(X^2) who´s minimum homogenous weight is 312.

Homogenous weight enumerator: w(x)=1x^0+98x^312+616x^319+483x^320+448x^322+448x^323+2128x^325+6328x^327+812x^328+448x^329+3136x^330+4032x^331+7056x^333+14952x^335+609x^336+6272x^337+3136x^338+19264x^339+22512x^341+34664x^343+644x^344+21952x^345+21952x^346+33600x^347+25648x^349+29456x^351+399x^352+378x^360+371x^368+182x^376+105x^384+14x^392

The gray image is a linear code over GF(8) with n=392, k=6 and d=312.
This code was found by Heurico 1.16 in 11.4 seconds.