The generator matrix

 1  0  1
 0  1 a^6*X+1

generates a code of length 3 over F8[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+168x^14+21x^16+2688x^21+1176x^22+42x^24

The gray image is a linear code over GF(8) with n=24, k=4 and d=14.
This code was found by Heurico 1.16 in 5.91e-005 seconds.