The generator matrix

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

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+126x^224+56x^226+1491x^232+1960x^234+896x^238+11270x^240+7224x^242+12544x^246+48601x^248+22456x^250+43904x^254+84707x^256+25648x^258+469x^264+462x^272+287x^280+42x^288

The gray image is a linear code over GF(8) with n=288, k=6 and d=224.
This code was found by Heurico 1.16 in 7.7 seconds.