The generator matrix

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

generates a code of length 11 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+96x^31+39x^32+96x^35+24x^36

The gray image is a linear code over GF(4) with n=44, k=4 and d=31.
This code was found by Heurico 1.16 in 0 seconds.