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  1  X a*X  1  1  1  0  1  1 a*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 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 X+a a*X+1  0  1 a*X X+a^2 a^2*X  1 X+a^2 a*X+a  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 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 X+a  1  1 a^2*X a*X+1 X+1 a*X+a^2 a*X  X a^2 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^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  0  X  X a*X  X a*X  0 a^2*X  X  0 a^2*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+720x^166+504x^167+168x^168+1776x^170+1272x^171+249x^172+1800x^174+1572x^175+162x^176+1908x^178+1116x^179+195x^180+1500x^182+924x^183+108x^184+948x^186+636x^187+111x^188+444x^190+120x^191+9x^192+120x^194+21x^196

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 11 seconds.