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

generates a code of length 60 over F8[X]/(X^2) who´s minimum homogenous weight is 408.

Homogenous weight enumerator: w(x)=1x^0+28x^408+560x^409+3360x^410+1176x^411+4704x^412+266x^416+1120x^417+4032x^418+784x^419+1344x^420+147x^424+1904x^425+6944x^426+1624x^427+4704x^428+49x^432+7x^440+14x^456

The gray image is a linear code over GF(8) with n=480, k=5 and d=408.
This code was found by Heurico 1.16 in 0.237 seconds.