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

generates a code of length 40 over F8[X]/(X^2) who´s minimum homogenous weight is 240.

Homogenous weight enumerator: w(x)=1x^0+329x^240+1680x^248+2674x^256+3318x^264+3584x^266+4529x^272+50176x^274+5733x^280+175616x^282+5978x^288+5040x^296+2492x^304+917x^312+77x^320

The gray image is a linear code over GF(8) with n=320, k=6 and d=240.
This code was found by Heurico 1.16 in 23.3 seconds.