The generator matrix

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

generates a code of length 55 over F8[X]/(X^2) who´s minimum homogenous weight is 360.

Homogenous weight enumerator: w(x)=1x^0+588x^360+560x^366+6440x^367+3990x^368+2800x^374+21000x^375+9212x^376+10640x^382+67704x^383+23548x^384+14672x^390+76888x^391+22974x^392+364x^400+315x^408+245x^416+168x^424+28x^432+7x^440

The gray image is a linear code over GF(8) with n=440, k=6 and d=360.
This code was found by Heurico 1.16 in 28.7 seconds.