The generator matrix

 1  0  1  1  1  1  1  1  1  0  1
 0  1  1  a a+1  0 (a+1)X+1  a (a+1)X+a+1  1 (a+1)X+1
 0  0 (a+1)X  0  0  X  0  X  X (a+1)X (a+1)X
 0  0  0  X  0 (a+1)X (a+1)X (a+1)X aX (a+1)X (a+1)X
 0  0  0  0 (a+1)X  X (a+1)X aX (a+1)X aX (a+1)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+213x^24+768x^27+597x^28+4608x^31+1461x^32+6912x^35+1626x^36+165x^40+33x^44

The gray image is a linear code over GF(4) with n=44, k=7 and d=24.
This code was found by Heurico 1.16 in 0.109 seconds.