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

generates a code of length 54 over F8[X]/(X^2) who´s minimum homogenous weight is 352.

Homogenous weight enumerator: w(x)=1x^0+399x^352+56x^353+168x^354+1624x^359+4774x^360+1512x^361+2296x^362+8568x^367+15183x^368+4536x^369+4648x^370+31752x^375+45430x^376+11256x^377+11816x^378+44072x^383+51898x^384+11312x^385+9744x^386+357x^392+266x^400+224x^408+168x^416+63x^424+21x^432

The gray image is a linear code over GF(8) with n=432, k=6 and d=352.
This code was found by Heurico 1.16 in 12.6 seconds.