The generator matrix

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

generates a code of length 59 over F4[X]/(X^2) who´s minimum homogenous weight is 173.

Homogenous weight enumerator: w(x)=1x^0+120x^173+252x^174+27x^176+192x^177+288x^178+18x^180+48x^181+12x^184+6x^188+24x^189+36x^190

The gray image is a linear code over GF(4) with n=236, k=5 and d=173.
This code was found by Heurico 1.16 in 0.047 seconds.