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^2*X a^2*X a^2*X a^2*X a^2*X  0 a*X a^2*X  0  X  0  X a^2*X  X
 0  0  X  0 a^2*X  X a^2*X  0 a^2*X a^2*X  X  X a^2*X  0  0  X a^2*X a^2*X  X  X a*X  0
 0  0  0  X  X  X a*X a^2*X  0  X  0  X a*X a*X a*X a*X a*X  0 a*X  X  X  0

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