The generator matrix

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

generates a code of length 13 over F8[X]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+1848x^77+2520x^78+105x^80+2688x^84+25872x^85+15120x^86+231x^88+68096x^91+18816x^92+90552x^93+36120x^94+42x^96+133x^104

The gray image is a linear code over GF(8) with n=104, k=6 and d=77.
This code was found by Heurico 1.16 in 1.63 seconds.