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

generates a code of length 57 over F8[X]/(X^2) who´s minimum homogenous weight is 382.

Homogenous weight enumerator: w(x)=1x^0+3248x^382+5600x^383+3598x^384+56x^385+672x^386+672x^387+2240x^388+6608x^389+13888x^390+21504x^391+9135x^392+784x^393+4032x^394+2240x^395+4480x^396+8288x^397+22064x^398+29792x^399+11949x^400+2744x^401+9632x^402+4256x^403+7616x^404+13776x^405+28896x^406+32704x^407+11592x^408+28x^416+14x^424+28x^432+7x^440

The gray image is a linear code over GF(8) with n=456, k=6 and d=382.
This code was found by Heurico 1.16 in 10.9 seconds.