The generator matrix

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

generates a code of length 46 over F8[X]/(X^2) who´s minimum homogenous weight is 296.

Homogenous weight enumerator: w(x)=1x^0+273x^296+798x^304+630x^312+686x^320+28672x^322+609x^328+364x^336+308x^344+315x^352+84x^360+28x^368

The gray image is a linear code over GF(8) with n=368, k=5 and d=296.
This code was found by Heurico 1.16 in 0.456 seconds.