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

generates a code of length 46 over F8[X]/(X^2) who´s minimum homogenous weight is 312.

Homogenous weight enumerator: w(x)=1x^0+119x^312+231x^320+3584x^322+133x^328+7x^352+21x^368

The gray image is a linear code over GF(8) with n=368, k=4 and d=312.
This code was found by Heurico 1.16 in 0.0174 seconds.