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

generates a code of length 56 over F4[X]/(X^2) who´s minimum homogenous weight is 166.

Homogenous weight enumerator: w(x)=1x^0+132x^166+33x^168+48x^170+24x^172+3x^176+12x^182+3x^184

The gray image is a linear code over GF(4) with n=224, k=4 and d=166.
This code was found by Heurico 1.16 in 0.031 seconds.