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

generates a code of length 56 over F8[X]/(X^2) who´s minimum homogenous weight is 360.

Homogenous weight enumerator: w(x)=1x^0+91x^360+728x^367+903x^368+448x^372+504x^373+1120x^374+4760x^375+5145x^376+4032x^380+2968x^381+3360x^382+12712x^383+10143x^384+19264x^388+10472x^389+11424x^390+32648x^391+24045x^392+33600x^396+14728x^397+12768x^398+35168x^399+20055x^400+378x^408+280x^416+182x^424+140x^432+63x^440+14x^448

The gray image is a linear code over GF(8) with n=448, k=6 and d=360.
This code was found by Heurico 1.16 in 13.3 seconds.