The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  1  1  1  1  1
 0  1  1  a (a+1)X+a+1  0 (a+1)X+1  a (a+1)X+a+1  1  0  a (a+1)X+1  1  X X+a  X aX+a (a+1)X+1 aX+1 (a+1)X+1  0
 0  0 (a+1)X  0  X  X (a+1)X  X (a+1)X  X  0  0  X  X aX  0  0 (a+1)X (a+1)X aX aX  0
 0  0  0  X aX  X aX (a+1)X (a+1)X  0  X (a+1)X  0 aX  X  0 aX  X (a+1)X aX  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+102x^56+12x^57+108x^59+384x^60+108x^61+156x^63+657x^64+324x^65+324x^67+1020x^68+324x^69+180x^71+354x^72+24x^76+6x^80+12x^84

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 0.0259 seconds.