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

generates a code of length 40 over F8[X]/(X^2) who´s minimum homogenous weight is 256.

Homogenous weight enumerator: w(x)=1x^0+343x^256+847x^264+714x^272+3584x^273+595x^280+25088x^281+567x^288+441x^296+364x^304+189x^312+35x^320

The gray image is a linear code over GF(8) with n=320, k=5 and d=256.
This code was found by Heurico 1.16 in 0.378 seconds.