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

generates a code of length 40 over F8[X]/(X^2) who´s minimum homogenous weight is 269.

Homogenous weight enumerator: w(x)=1x^0+3360x^269+2520x^270+189x^272+6720x^277+3024x^278+224x^280+11424x^285+5208x^286+63x^288+7x^304+28x^320

The gray image is a linear code over GF(8) with n=320, k=5 and d=269.
This code was found by Heurico 1.16 in 15.5 seconds.