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

generates a code of length 59 over F4[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+153x^168+168x^170+504x^171+498x^172+288x^174+456x^175+510x^176+108x^178+144x^179+162x^180+12x^182+192x^183+315x^184+156x^186+216x^187+126x^188+36x^190+24x^191+15x^192+6x^196+6x^200

The gray image is a linear code over GF(4) with n=236, k=6 and d=168.
This code was found by Heurico 1.16 in 0.104 seconds.