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

generates a code of length 74 over F8[X]/(X^2) who´s minimum homogenous weight is 501.

Homogenous weight enumerator: w(x)=1x^0+448x^501+3472x^502+12488x^503+8932x^504+2464x^505+1008x^509+11928x^510+31640x^511+20573x^512+4480x^513+2912x^517+15904x^518+36344x^519+17766x^520+3360x^521+2800x^525+18872x^526+41384x^527+21322x^528+4032x^529+14x^536

The gray image is a linear code over GF(8) with n=592, k=6 and d=501.
This code was found by Heurico 1.16 in 70.9 seconds.