The generator matrix

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

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+714x^16+2688x^18+2016x^20+16128x^22+16392x^24+24192x^26+3360x^28+45x^32

The gray image is a linear code over GF(4) with n=32, k=8 and d=16.
This code was found by Heurico 1.16 in 0.493 seconds.