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.