The generator matrix

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

generates a code of length 68 over F8[X]/(X^2) who´s minimum homogenous weight is 448.

Homogenous weight enumerator: w(x)=1x^0+210x^448+56x^450+168x^452+3808x^455+1043x^456+560x^457+2968x^458+2296x^460+10696x^463+2807x^464+2800x^465+10920x^466+4648x^468+18984x^471+10269x^472+10640x^473+33544x^474+11816x^476+32984x^479+17185x^480+14672x^481+38528x^482+9744x^484+19544x^487+357x^488+266x^496+231x^504+161x^512+168x^520+35x^528+28x^536+7x^544

The gray image is a linear code over GF(8) with n=544, k=6 and d=448.
This code was found by Heurico 1.16 in 16.9 seconds.