The generator matrix

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

generates a code of length 78 over F8[X]/(X^2) who´s minimum homogenous weight is 526.

Homogenous weight enumerator: w(x)=1x^0+2520x^526+553x^528+1568x^529+2576x^530+2352x^531+2744x^532+7000x^533+16408x^534+560x^535+2597x^536+7784x^537+9240x^538+5376x^539+6552x^540+11704x^541+21784x^542+1120x^543+4578x^544+11088x^545+13216x^546+6384x^547+5544x^548+9800x^549+26152x^550+1904x^551+6930x^552+15400x^553+14392x^554+7392x^555+6664x^556+10920x^557+19152x^558+77x^560+70x^568+28x^576+7x^584+7x^592

The gray image is a linear code over GF(8) with n=624, k=6 and d=526.
This code was found by Heurico 1.16 in 16.5 seconds.