The generator matrix

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

generates a code of length 11 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+120x^22+597x^24+480x^26+1536x^27+4053x^28+3216x^30+9216x^31+11829x^32+7008x^34+13824x^35+11994x^36+1464x^38+165x^40+33x^44

The gray image is a linear code over GF(4) with n=44, k=8 and d=22.
This code was found by Heurico 1.16 in 1.25 seconds.