The generator matrix

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

generates a code of length 57 over F4[X]/(X^2) who´s minimum homogenous weight is 160.

Homogenous weight enumerator: w(x)=1x^0+1077x^160+3171x^164+3255x^168+3486x^172+2805x^176+1878x^180+645x^184+54x^188+9x^192+3x^196

The gray image is a linear code over GF(4) with n=228, k=7 and d=160.
This code was found by Heurico 1.16 in 0.922 seconds.