The generator matrix

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

generates a code of length 53 over F8[X]/(X^2) who´s minimum homogenous weight is 360.

Homogenous weight enumerator: w(x)=1x^0+3444x^360+1176x^362+3136x^363+6972x^368+784x^370+896x^371+11515x^376+1624x^378+3136x^379+56x^384+7x^392+7x^400+14x^408

The gray image is a linear code over GF(8) with n=424, k=5 and d=360.
This code was found by Heurico 1.16 in 0.168 seconds.