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

generates a code of length 28 over F8[X]/(X^2) who´s minimum homogenous weight is 160.

Homogenous weight enumerator: w(x)=1x^0+350x^160+1582x^168+2968x^176+4032x^184+28672x^189+6055x^192+200704x^197+7518x^200+6412x^208+3220x^216+630x^224

The gray image is a linear code over GF(8) with n=224, k=6 and d=160.
This code was found by Heurico 1.16 in 14.6 seconds.