The generator matrix

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

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+108x^60+45x^64+768x^66+39x^68+15x^72+30x^76+15x^84+3x^88

The gray image is a linear code over GF(4) with n=88, k=5 and d=60.
This code was found by Heurico 1.16 in 0.031 seconds.