The generator matrix

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

generates a code of length 60 over F4[X]/(X^2) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+444x^165+780x^166+360x^167+828x^168+1884x^169+2340x^170+1116x^171+1686x^172+2964x^173+3324x^174+1836x^175+2046x^176+3864x^177+4968x^178+1584x^179+2466x^180+4656x^181+4980x^182+2052x^183+2379x^184+4464x^185+3660x^186+1488x^187+1590x^188+2424x^189+2412x^190+696x^191+735x^192+684x^193+552x^194+84x^195+42x^196+120x^197+24x^198+3x^200

The gray image is a linear code over GF(4) with n=240, k=8 and d=165.
This code was found by Heurico 1.16 in 16.5 seconds.