The generator matrix

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

generates a code of length 12 over F8[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+672x^78+42x^80+1344x^84+2016x^86+21x^96

The gray image is a linear code over GF(8) with n=96, k=4 and d=78.
This code was found by Heurico 1.16 in 0.00846 seconds.