The generator matrix

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

generates a code of length 56 over F4[X]/(X^2) who´s minimum homogenous weight is 160.

Homogenous weight enumerator: w(x)=1x^0+624x^160+1263x^164+837x^168+558x^172+492x^176+291x^180+21x^184+9x^192

The gray image is a linear code over GF(4) with n=224, k=6 and d=160.
This code was found by Heurico 1.16 in 0.098 seconds.