The generator matrix

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

generates a code of length 22 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+303x^60+372x^61+396x^62+501x^64+564x^65+360x^66+192x^68+444x^69+396x^70+402x^72+156x^73+9x^76

The gray image is a linear code over GF(4) with n=88, k=6 and d=60.
This code was found by Heurico 1.16 in 0.016 seconds.