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

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+261x^172+168x^173+396x^175+1050x^176+192x^177+180x^179+426x^180+144x^181+333x^184+192x^185+216x^188+72x^189+180x^191+258x^192+12x^195+6x^196+3x^200+3x^204+3x^208

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 0.106 seconds.