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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  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 a^6*X+a^6 X+a^3 X+a^5 a^5*X+a^6 X+a^5 X+a a*X+a a^5*X+a^6 a^6*X+1 a^5*X+1 a^4*X+a^5 a*X+a a^6 a^6*X+1 a*X+a X+1  0 a^3*X+a^6 X+a^5 a^3*X+1 a^2*X+a a^2*X+a^6 a*X+a^5 a^4*X+1  a
 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*X a^3*X a^6*X a^5*X  0 a^4*X a^6*X a^4*X a^4*X a^2*X a^5*X a*X  0 a^6*X  X a^5*X a*X a^5*X a^6*X  0 a^2*X a^2*X a^4*X a^6*X a^3*X
 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^6*X a^2*X a^2*X a^2*X a*X a^5*X a^3*X a^6*X a^3*X a^6*X a^5*X a^2*X  0  X a^3*X  0  0  X a^5*X a^6*X  X a^3*X a^3*X a*X a^3*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+826x^312+1008x^313+112x^315+224x^316+5334x^320+4648x^321+896x^322+2352x^323+2016x^324+10059x^328+12264x^329+12544x^330+16464x^331+9632x^332+24164x^336+22008x^337+43904x^338+38416x^339+16800x^340+19985x^344+17416x^345+420x^352+301x^360+252x^368+77x^376+21x^384

The gray image is a linear code over GF(8) with n=384, k=6 and d=312.
This code was found by Heurico 1.16 in 11.1 seconds.