The generator matrix

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

generates a code of length 59 over F4[X]/(X^2) who´s minimum homogenous weight is 169.

Homogenous weight enumerator: w(x)=1x^0+264x^169+180x^170+372x^171+294x^172+384x^173+300x^174+204x^175+228x^176+240x^177+228x^178+132x^179+165x^180+156x^181+120x^182+72x^183+87x^184+180x^185+96x^186+144x^187+27x^188+84x^189+36x^190+36x^191+24x^192+36x^193+6x^196

The gray image is a linear code over GF(4) with n=236, k=6 and d=169.
This code was found by Heurico 1.16 in 0.094 seconds.