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

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+175x^376+112x^380+168x^381+504x^383+2177x^384+560x^387+2632x^388+3136x^389+2352x^391+7084x^392+2800x^395+11592x^396+8400x^397+6048x^399+12173x^400+10640x^403+32984x^404+23296x^405+11088x^407+23800x^408+14672x^411+38696x^412+22344x^413+8680x^415+15050x^416+322x^424+301x^432+189x^440+98x^448+70x^456

The gray image is a linear code over GF(8) with n=464, k=6 and d=376.
This code was found by Heurico 1.16 in 14.1 seconds.