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

generates a code of length 46 over F8[X]/(X^2) who´s minimum homogenous weight is 311.

Homogenous weight enumerator: w(x)=1x^0+4480x^311+938x^312+8960x^319+1267x^320+15232x^327+1862x^328+7x^336+21x^368

The gray image is a linear code over GF(8) with n=368, k=5 and d=311.
This code was found by Heurico 1.16 in 0.159 seconds.