The generator matrix

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

generates a code of length 60 over F4[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+147x^168+612x^169+708x^171+675x^172+1452x^173+984x^175+870x^176+1536x^177+948x^179+837x^180+1632x^181+876x^183+726x^184+1152x^185+696x^187+603x^188+792x^189+300x^191+189x^192+396x^193+96x^195+39x^196+108x^197+3x^200+6x^204

The gray image is a linear code over GF(4) with n=240, k=7 and d=168.
This code was found by Heurico 1.16 in 0.829 seconds.