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

generates a code of length 54 over F8[X]/(X^2) who´s minimum homogenous weight is 336.

Homogenous weight enumerator: w(x)=1x^0+532x^336+1981x^344+2429x^352+3374x^360+3584x^364+4095x^368+50176x^372+4354x^376+175616x^380+5145x^384+4508x^392+3654x^400+1785x^408+777x^416+126x^424+7x^432

The gray image is a linear code over GF(8) with n=432, k=6 and d=336.
This code was found by Heurico 1.16 in 33.7 seconds.