The generator matrix

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

generates a code of length 60 over F8[X]/(X^2) who´s minimum homogenous weight is 403.

Homogenous weight enumerator: w(x)=1x^0+4424x^403+6328x^404+1512x^405+168x^407+28x^408+27888x^411+30912x^412+3752x^413+1008x^415+224x^416+40712x^419+37464x^420+4088x^421+2408x^423+245x^424+52416x^427+43568x^428+4984x^429+7x^456+7x^480

The gray image is a linear code over GF(8) with n=480, k=6 and d=403.
This code was found by Heurico 1.16 in 11.7 seconds.