The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X 1
0 X 0 0 0 0 X X X aX aX (a+1)X 0 X (a+1)X X 0 aX X (a+1)X X 0
0 0 X 0 0 X (a+1)X (a+1)X aX 0 (a+1)X 0 aX X X (a+1)X X aX X X aX aX
0 0 0 X 0 (a+1)X 0 (a+1)X X aX (a+1)X aX (a+1)X X aX X aX (a+1)X X X 0 X
0 0 0 0 X X X (a+1)X (a+1)X (a+1)X aX X (a+1)X (a+1)X aX 0 (a+1)X 0 aX X 0 0
generates a code of length 22 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 56.
Homogenous weight enumerator: w(x)=1x^0+264x^56+192x^60+1515x^64+1728x^68+264x^72+132x^80
The gray image is a linear code over GF(4) with n=88, k=6 and d=56.
This code was found by Heurico 1.16 in 49.8 seconds.