The generator matrix

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

generates a code of length 54 over F8[X]/(X^2) who´s minimum homogenous weight is 361.

Homogenous weight enumerator: w(x)=1x^0+2912x^361+6776x^362+56x^364+336x^365+672x^366+5600x^367+6069x^368+18312x^369+21784x^370+448x^371+784x^372+2016x^373+2240x^374+11200x^375+7217x^376+26768x^377+32872x^378+3136x^379+2744x^380+4816x^381+4256x^382+19040x^383+12201x^384+34440x^385+35336x^386+70x^392+14x^400+14x^408+7x^416+7x^424

The gray image is a linear code over GF(8) with n=432, k=6 and d=361.
This code was found by Heurico 1.16 in 99.5 seconds.