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

generates a code of length 58 over F4[X]/(X^2) who´s minimum homogenous weight is 166.

Homogenous weight enumerator: w(x)=1x^0+600x^166+336x^168+756x^170+261x^172+636x^174+141x^176+444x^178+156x^180+420x^182+105x^184+192x^186+12x^188+24x^190+6x^192+3x^200+3x^204

The gray image is a linear code over GF(4) with n=232, k=6 and d=166.
This code was found by Heurico 1.16 in 92.1 seconds.