The generator matrix

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

generates a code of length 57 over F8[X]/(X^2) who´s minimum homogenous weight is 389.

Homogenous weight enumerator: w(x)=1x^0+5880x^389+1176x^390+1568x^391+147x^392+7056x^397+784x^398+448x^399+301x^400+12152x^405+1624x^406+1568x^407+49x^408+14x^448

The gray image is a linear code over GF(8) with n=456, k=5 and d=389.
This code was found by Heurico 1.16 in 23.7 seconds.