The generator matrix

 1  1  1  1
 0  X  0  X
 0  0  X a^6*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+168x^24+3584x^28+301x^32

The gray image is a linear code over GF(8) with n=32, k=4 and d=16.
This code was found by Heurico 1.16 in 0.000193 seconds.