The generator matrix

 1  0  0  1  1  1  1  1
 0  1  0  1 (a+1)X (a+1)X  a a+1
 0  0  1 a+1 a+1 X+a+1  a  1
 0  0  0  X aX (a+1)X  0 aX

generates a code of length 8 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+174x^16+672x^18+480x^20+4032x^22+4176x^24+6048x^26+768x^28+33x^32

The gray image is a linear code over GF(4) with n=32, k=7 and d=16.
This code was found by Heurico 1.16 in 0.0427 seconds.