The generator matrix

 1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  X  0  X  X (a+1)X (a+1)X  0
 0  0  X  0 (a+1)X  X (a+1)X  0 (a+1)X (a+1)X  0
 0  0  0  X  X  X aX (a+1)X  0  X  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+30x^24+66x^28+39x^32+768x^33+60x^36+42x^40+18x^44

The gray image is a linear code over GF(4) with n=44, k=5 and d=24.
This code was found by Heurico 1.16 in 0 seconds.