The generator matrix

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

generates a code of length 52 over F8[X]/(X^2) who´s minimum homogenous weight is 352.

Homogenous weight enumerator: w(x)=1x^0+1113x^352+1120x^353+784x^354+4704x^356+3542x^360+2240x^361+1120x^362+1344x^364+6524x^368+3808x^369+1680x^370+4704x^372+14x^376+42x^384+28x^392

The gray image is a linear code over GF(8) with n=416, k=5 and d=352.
This code was found by Heurico 1.16 in 0.164 seconds.