The generator matrix

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

generates a code of length 55 over F4[X]/(X^2) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+252x^146+492x^147+453x^148+1140x^149+1776x^150+3072x^151+1905x^152+3240x^153+4284x^154+6636x^155+3858x^156+6768x^157+9576x^158+12060x^159+6000x^160+10896x^161+14508x^162+18420x^163+9288x^164+14796x^165+18264x^166+21108x^167+10566x^168+13560x^169+15444x^170+15684x^171+6336x^172+8232x^173+7944x^174+7236x^175+2136x^176+2544x^177+1608x^178+1200x^179+324x^180+264x^181+72x^182+108x^183+30x^184+36x^188+9x^192+9x^196+9x^200

The gray image is a linear code over GF(4) with n=220, k=9 and d=146.
This code was found by Heurico 1.16 in 200 seconds.