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

generates a code of length 71 over F8[X]/(X^2) who´s minimum homogenous weight is 448.

Homogenous weight enumerator: w(x)=1x^0+203x^448+1253x^456+2072x^464+2947x^472+3542x^480+3584x^483+3703x^488+50176x^491+3927x^496+175616x^499+4123x^504+3906x^512+3206x^520+2205x^528+1085x^536+434x^544+140x^552+14x^560+7x^568

The gray image is a linear code over GF(8) with n=568, k=6 and d=448.
This code was found by Heurico 1.16 in 46.2 seconds.