The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  X  1  1  1 a^2*X  1  1  1  1  0  1  X  1 a*X  1  1  1  1 a^2*X  1  1  1 a^2*X  1 a*X  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  X  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  1 a*X+a X+1 X+a  1 X+a^2  a a^2*X+a^2 a*X+a^2  1  a  1  0  1 a*X+1 a^2*X X+a^2 a^2  1 X+1 a^2*X+a  X  0  1  1 a*X+a^2 a^2*X+a^2  1 a^2  a a*X+1 a*X  0 a^2*X X+1  X a^2*X+a^2 a*X+1 a^2*X  a  1 X+a^2  1 a^2*X+a a^2*X+a^2 a^2*X+a  1
 0  0  1  1  a a^2 X+a^2 a^2*X+a^2 a*X+a^2 X+a a*X+1 a^2*X+a^2 X+1  X a^2*X+a a*X+1 a*X+a  0 a^2*X+1 a*X X+a  X a^2*X+a a*X a^2*X+1 X+a^2 a^2*X+1 a*X+1 a*X+a  X X+a a^2*X+a a^2*X+a^2  1 a*X+a^2 X+1 a^2*X+1 a^2*X+a^2 a^2*X a^2*X a*X+1 a^2*X+a  X a^2*X+1  1 a*X+a^2  X  0  1  a  1 a*X+1 X+1 X+a a*X+a a*X+a^2 X+a^2 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+204x^166+204x^167+336x^168+288x^169+504x^170+228x^171+273x^172+216x^173+324x^174+96x^175+159x^176+144x^177+252x^178+108x^179+96x^180+60x^181+108x^182+60x^183+96x^184+24x^185+132x^186+72x^187+63x^188+36x^189+12x^190

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 0.078 seconds.