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

generates a code of length 28 over F8[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+168x^168+336x^175+1505x^176+448x^182+7056x^183+5866x^184+6272x^190+49392x^191+15932x^192+21952x^198+115248x^199+36596x^200+679x^208+602x^216+91x^224

The gray image is a linear code over GF(8) with n=224, k=6 and d=168.
This code was found by Heurico 1.16 in 5.58 seconds.