The generator matrix

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

generates a code of length 60 over F4[X]/(X^2) who´s minimum homogenous weight is 161.

Homogenous weight enumerator: w(x)=1x^0+444x^161+732x^162+576x^163+1254x^164+2316x^165+3384x^166+1860x^167+3294x^168+6096x^169+6324x^170+3336x^171+6117x^172+10200x^173+11460x^174+5652x^175+10920x^176+16296x^177+15900x^178+7980x^179+14034x^180+21036x^181+18072x^182+8772x^183+13173x^184+17520x^185+14988x^186+5952x^187+7539x^188+9120x^189+7140x^190+2220x^191+2616x^192+2748x^193+1704x^194+492x^195+348x^196+240x^197+168x^198+24x^199+33x^200+30x^204+18x^208+6x^212+6x^216+3x^224

The gray image is a linear code over GF(4) with n=240, k=9 and d=161.
This code was found by Heurico 1.16 in 320 seconds.