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

generates a code of length 52 over F8[X]/(X^2) who´s minimum homogenous weight is 336.

Homogenous weight enumerator: w(x)=1x^0+189x^336+112x^338+56x^339+959x^344+1120x^345+3864x^346+3472x^347+2730x^352+5600x^353+14616x^354+8064x^355+10311x^360+21280x^361+44744x^362+23408x^363+17283x^368+29344x^369+51352x^370+22344x^371+371x^376+399x^384+245x^392+238x^400+42x^408

The gray image is a linear code over GF(8) with n=416, k=6 and d=336.
This code was found by Heurico 1.16 in 12.3 seconds.