The generator matrix

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

generates a code of length 11 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+78x^24+192x^27+207x^28+1152x^31+195x^32+1728x^35+474x^36+54x^40+15x^44

The gray image is a linear code over GF(4) with n=44, k=6 and d=24.
This code was found by Heurico 1.16 in 0.0088 seconds.