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

generates a code of length 53 over F8[X]/(X^2) who´s minimum homogenous weight is 328.

Homogenous weight enumerator: w(x)=1x^0+399x^328+1701x^336+2387x^344+3325x^352+3584x^357+3927x^360+50176x^365+4585x^368+175616x^373+4865x^376+4907x^384+3661x^392+2044x^400+770x^408+189x^416+7x^424

The gray image is a linear code over GF(8) with n=424, k=6 and d=328.
This code was found by Heurico 1.16 in 32.4 seconds.