The generator matrix

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

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+165x^24+165x^28+165x^32+3072x^33+330x^36+165x^40+33x^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 0.0138 seconds.