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

generates a code of length 41 over F8[X]/(X^2) who´s minimum homogenous weight is 276.

Homogenous weight enumerator: w(x)=1x^0+2800x^276+3360x^277+231x^280+5600x^284+4032x^285+196x^288+9520x^292+6944x^293+49x^296+7x^304+28x^328

The gray image is a linear code over GF(8) with n=328, k=5 and d=276.
This code was found by Heurico 1.16 in 41.6 seconds.