The generator matrix

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

generates a code of length 11 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+165x^20+588x^24+3072x^27+2223x^28+18432x^31+6339x^32+27648x^35+6339x^36+528x^40+201x^44

The gray image is a linear code over GF(4) with n=44, k=8 and d=20.
This code was found by Heurico 1.16 in 1.44 seconds.