The generator matrix

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

generates a code of length 60 over F4[X]/(X^2) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+210x^172+348x^173+228x^174+690x^176+492x^177+252x^178+300x^180+276x^181+84x^182+216x^184+168x^185+108x^186+222x^188+132x^189+72x^190+117x^192+108x^193+24x^194+36x^196+12x^197

The gray image is a linear code over GF(4) with n=240, k=6 and d=172.
This code was found by Heurico 1.16 in 0.079 seconds.