The generator matrix

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

generates a code of length 4 over F8[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+42x^16+1792x^21+168x^24+17920x^28+12544x^29+301x^32

The gray image is a linear code over GF(8) with n=32, k=5 and d=16.
This code was found by Heurico 1.16 in 0.00366 seconds.