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

generates a code of length 27 over F8[X]/(X^2) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+371x^176+2016x^177+560x^178+2317x^184+6720x^185+1120x^186+4914x^192+12768x^193+1904x^194+7x^200+14x^208+56x^216

The gray image is a linear code over GF(8) with n=216, k=5 and d=176.
This code was found by Heurico 1.16 in 0.0868 seconds.