The generator matrix

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

generates a code of length 5 over F8[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+70x^16+448x^21+420x^24+10752x^28+6272x^29+1505x^32+143360x^35+75264x^36+21952x^37+2100x^40

The gray image is a linear code over GF(8) with n=40, k=6 and d=16.
This code was found by Heurico 1.16 in 0.221 seconds.