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

generates a code of length 39 over F8[X]/(X^2) who´s minimum homogenous weight is 248.

Homogenous weight enumerator: w(x)=1x^0+259x^248+56x^252+798x^256+1176x^260+728x^264+8232x^268+679x^272+19208x^276+546x^280+413x^288+448x^296+189x^304+35x^312

The gray image is a linear code over GF(8) with n=312, k=5 and d=248.
This code was found by Heurico 1.16 in 0.375 seconds.