The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1
0 X 0 0 X X a*X a^2*X 0 a^2*X a^4*X X a*X
0 0 X 0 a^6*X a^5*X a*X a^6*X a^2*X a^6*X a^3*X a^3*X a*X
0 0 0 X X a^4*X a^4*X X X a^4*X 0 a^6*X a^3*X
generates a code of length 13 over F8[X]/(X^2) who´s minimum homogenous weight is 72.
Homogenous weight enumerator: w(x)=1x^0+322x^72+714x^80+840x^88+28672x^91+1533x^96+686x^104
The gray image is a linear code over GF(8) with n=104, k=5 and d=72.
This code was found by Heurico 1.16 in 0.114 seconds.