The generator matrix

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

generates a code of length 14 over F8[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+924x^72+2387x^80+4144x^88+10507x^96+229376x^98+9716x^104+5089x^112

The gray image is a linear code over GF(8) with n=112, k=6 and d=72.
This code was found by Heurico 1.16 in 4.97 seconds.