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^2*X+a^2  0 a^2*X+1 a^2*X+a^2  X  a  1 a^2*X+1  1  X a*X+a^2  1 X+a X+a a*X+a^2  1 a^2*X a^2*X
 0  0 a^2*X a*X  X  X  0 a^2*X a*X a^2*X a^2*X  X a*X  X a*X a*X  0  X  0  X a*X  0

generates a code of length 22 over F4[X]/(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 0.046 seconds.