The generator matrix

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

generates a code of length 57 over F4[X]/(X^2) who´s minimum homogenous weight is 164.

Homogenous weight enumerator: w(x)=1x^0+279x^164+708x^165+252x^166+84x^167+378x^168+540x^169+120x^170+60x^171+186x^172+336x^173+96x^174+36x^175+150x^176+264x^177+48x^178+144x^180+156x^181+36x^182+75x^184+108x^185+24x^186+12x^187+3x^188

The gray image is a linear code over GF(4) with n=228, k=6 and d=164.
This code was found by Heurico 1.16 in 22 seconds.