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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  X  X a*X a^2*X a^4*X a^5*X a^5*X  X a^5*X a^6*X  0 a*X a^5*X a*X a^5*X a^6*X a^6*X a^2*X  0 a*X a*X a^3*X a^4*X a^5*X a^5*X  X  X  X a*X a^6*X a^6*X  0  0 a*X a^3*X a^6*X a^4*X  0 a^4*X a^4*X a*X a*X  X  0 a*X  X  X a^5*X  0 a^5*X a^2*X  X  0
 0  0  X  0 a^6*X a^5*X a*X a^6*X a^6*X a*X a^6*X a^2*X a*X a^3*X  X a^5*X a^3*X a^4*X a^4*X  X a^4*X  0 a*X  X a*X a^6*X  0 a^3*X  X a^4*X a*X a^2*X a^6*X a*X a^2*X a^6*X  X  0  X a^2*X a^3*X a^5*X a^4*X a^3*X a^3*X  0 a*X a^2*X  X a*X a^4*X  0 a^6*X a^4*X a^5*X a^5*X  0
 0  0  0  X  X a^4*X a^4*X  X a^6*X a^4*X a^6*X a^6*X a^3*X a*X a^4*X a*X  0  0 a^6*X a^5*X a^6*X a^5*X  X a^5*X  X  X a^5*X a*X a^6*X  0 a^2*X a^4*X a^3*X a^4*X a^5*X a^6*X a^5*X  0 a^4*X a^4*X a^3*X a^6*X a^5*X a^6*X  X a*X  0 a*X a*X  X a^2*X a^2*X a*X  X a^5*X a^2*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+553x^376+847x^384+644x^392+28672x^399+504x^400+350x^408+434x^416+266x^424+245x^432+77x^440+70x^448+14x^456

The gray image is a linear code over GF(8) with n=456, k=5 and d=368.
This code was found by Heurico 1.16 in 0.589 seconds.