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

generates a code of length 69 over F8[X]/(X^2) who´s minimum homogenous weight is 456.

Homogenous weight enumerator: w(x)=1x^0+350x^456+448x^458+168x^459+1120x^462+2128x^463+756x^464+1120x^465+6048x^466+2352x^467+4200x^470+5936x^471+763x^472+3360x^473+16800x^474+4480x^475+5320x^478+16016x^479+644x^480+11424x^481+46816x^482+11984x^483+11704x^486+27664x^487+378x^488+12768x^489+44576x^490+9688x^491+6328x^494+5600x^495+364x^496+266x^504+196x^512+175x^520+98x^528+77x^536+21x^544+7x^552

The gray image is a linear code over GF(8) with n=552, k=6 and d=456.
This code was found by Heurico 1.16 in 17 seconds.