The generator matrix

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

generates a code of length 68 over F8[X]/(X^2) who´s minimum homogenous weight is 460.

Homogenous weight enumerator: w(x)=1x^0+9240x^460+9576x^461+1344x^462+168x^463+21x^464+38136x^468+25368x^469+3808x^470+1008x^471+189x^472+46536x^476+29400x^477+1792x^478+2408x^479+294x^480+56616x^484+32424x^485+3808x^486+7x^520

The gray image is a linear code over GF(8) with n=544, k=6 and d=460.
This code was found by Heurico 1.16 in 13.4 seconds.