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

generates a code of length 57 over F8[X]/(X^2) who´s minimum homogenous weight is 368.

Homogenous weight enumerator: w(x)=1x^0+91x^368+56x^371+168x^374+224x^375+1092x^376+56x^378+784x^379+2128x^381+4984x^382+2072x^383+3437x^384+1176x^386+3136x^387+7056x^389+12264x^390+4984x^391+5838x^392+8232x^394+5488x^395+22512x^397+35112x^398+11592x^399+12369x^400+19208x^402+19208x^403+25648x^405+33488x^406+9800x^407+8925x^408+315x^416+322x^424+196x^432+105x^440+63x^448+14x^456

The gray image is a linear code over GF(8) with n=456, k=6 and d=368.
This code was found by Heurico 1.16 in 13.6 seconds.