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

generates a code of length 59 over F4[X]/(X^2) who´s minimum homogenous weight is 166.

Homogenous weight enumerator: w(x)=1x^0+744x^166+528x^167+201x^168+1692x^170+1296x^171+165x^172+1956x^174+1320x^175+201x^176+1824x^178+1380x^179+246x^180+1380x^182+948x^183+99x^184+1056x^186+540x^187+48x^188+480x^190+132x^191+42x^192+84x^194+18x^196+3x^204

The gray image is a linear code over GF(4) with n=236, k=7 and d=166.
This code was found by Heurico 1.16 in 2.83 seconds.