The generator matrix

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

generates a code of length 22 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+288x^62+183x^64+192x^66+288x^70+72x^72

The gray image is a linear code over GF(4) with n=88, k=5 and d=62.
This code was found by Heurico 1.16 in 0.047 seconds.