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

generates a code of length 50 over F8[X]/(X^2) who´s minimum homogenous weight is 304.

Homogenous weight enumerator: w(x)=1x^0+140x^304+945x^312+2296x^320+2870x^328+3682x^336+28672x^343+4354x^344+200704x^351+5103x^352+5320x^360+4263x^368+2373x^376+1148x^384+266x^392+7x^400

The gray image is a linear code over GF(8) with n=400, k=6 and d=304.
This code was found by Heurico 1.16 in 29.9 seconds.