The generator matrix
1 0 1 1 1 1 1 1 1 0 X 1 1
0 1 1 a a^6*X+a^2 0 a^6*X+1 a a^6*X+a^2 1 X a^3 a^3
0 0 a^6*X a*X X a^2*X a^3*X a^5*X a^4*X a*X a^6*X 0 X
generates a code of length 13 over F8[X]/(X^2) who´s minimum homogenous weight is 78.
Homogenous weight enumerator: w(x)=1x^0+1008x^78+112x^80+1344x^84+6048x^86+210x^88+9408x^92+14448x^94+63x^96+126x^104
The gray image is a linear code over GF(8) with n=104, k=5 and d=78.
This code was found by Heurico 1.16 in 0.0349 seconds.