The generator matrix

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

generates a code of length 59 over F4[X]/(X^2) who´s minimum homogenous weight is 164.

Homogenous weight enumerator: w(x)=1x^0+162x^164+219x^168+192x^171+126x^172+1152x^175+114x^176+1728x^179+111x^180+90x^184+54x^188+33x^192+36x^196+30x^200+18x^204+6x^208+18x^212+3x^216+3x^228

The gray image is a linear code over GF(4) with n=236, k=6 and d=164.
This code was found by Heurico 1.16 in 2.03 seconds.