The generator matrix
1 0 1
0 1 a^6*X+1
0 0 X
generates a code of length 3 over F8[X]/(X^2) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+21x^8+1344x^14+147x^16+21504x^21+9408x^22+343x^24
The gray image is a linear code over GF(8) with n=24, k=5 and d=8.
This code was found by Heurico 1.16 in 0.00215 seconds.