The generator matrix

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

generates a code of length 27 over F8[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+504x^168+707x^176+3584x^182+763x^184+25088x^190+721x^192+742x^200+539x^208+119x^216

The gray image is a linear code over GF(8) with n=216, k=5 and d=168.
This code was found by Heurico 1.16 in 0.229 seconds.