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.