The generator matrix

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

generates a code of length 60 over F8[X]/(X^2) who´s minimum homogenous weight is 376.

Homogenous weight enumerator: w(x)=1x^0+420x^376+1757x^384+2450x^392+5033x^400+20020x^408+81347x^416+138838x^424+4263x^432+3892x^440+2471x^448+1204x^456+392x^464+56x^472

The gray image is a linear code over GF(8) with n=480, k=6 and d=376.
This code was found by Heurico 1.16 in 37.5 seconds.