The generator matrix

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

generates a code of length 56 over F8[X]/(X^2) who´s minimum homogenous weight is 382.

Homogenous weight enumerator: w(x)=1x^0+5880x^382+2352x^383+91x^384+7056x^390+1568x^391+357x^392+12152x^398+3248x^399+49x^400+7x^440+7x^448

The gray image is a linear code over GF(8) with n=448, k=5 and d=382.
This code was found by Heurico 1.16 in 0.893 seconds.