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

generates a code of length 55 over F4[X]/(X^2) who´s minimum homogenous weight is 163.

Homogenous weight enumerator: w(x)=1x^0+132x^163+27x^164+48x^167+21x^168+9x^172+6x^176+12x^179

The gray image is a linear code over GF(4) with n=220, k=4 and d=163.
This code was found by Heurico 1.16 in 0.078 seconds.