The generator matrix

 1  0  0  1  1  1 (a+1)X  1  1  1  1
 0  1  0  1  a a+1  1 (a+1)X (a+1)X+1 (a+1)X  0
 0  0  1 a+1  a  1  1  1  0 X+a+1  X
 0  0  0  X  0  X aX (a+1)X (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+132x^24+132x^25+108x^26+192x^27+1023x^28+468x^29+732x^30+1152x^31+2991x^32+1740x^33+2052x^34+1728x^35+2970x^36+732x^37+180x^38+36x^40+15x^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 0.0768 seconds.