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

generates a code of length 58 over F8[X]/(X^2) who´s minimum homogenous weight is 376.

Homogenous weight enumerator: w(x)=1x^0+105x^376+644x^384+819x^392+616x^400+28672x^406+497x^408+406x^416+378x^424+266x^432+224x^440+77x^448+49x^456+14x^464

The gray image is a linear code over GF(8) with n=464, k=5 and d=376.
This code was found by Heurico 1.16 in 0.604 seconds.