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

generates a code of length 61 over F4[X]/(X^2) who´s minimum homogenous weight is 180.

Homogenous weight enumerator: w(x)=1x^0+93x^180+768x^183+144x^184+15x^192+3x^244

The gray image is a linear code over GF(4) with n=244, k=5 and d=180.
This code was found by Heurico 1.16 in 0.031 seconds.