The generator matrix

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

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+24x^16+144x^18+72x^20+384x^21+864x^22+60x^24+1152x^25+1296x^26+72x^28+27x^32

The gray image is a linear code over GF(4) with n=32, k=6 and d=16.
This code was found by Heurico 1.16 in 0.00463 seconds.