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

generates a code of length 36 over F8[X]/(X^2) who´s minimum homogenous weight is 224.

Homogenous weight enumerator: w(x)=1x^0+147x^224+763x^232+2870x^240+10269x^248+17353x^256+581x^264+462x^272+259x^280+63x^288

The gray image is a linear code over GF(8) with n=288, k=5 and d=224.
This code was found by Heurico 1.16 in 0.339 seconds.