The generator matrix

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

generates a code of length 55 over F4[X]/(X^2) who´s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+129x^148+144x^149+132x^150+732x^151+867x^152+972x^153+660x^154+1920x^155+1875x^156+1668x^157+1356x^158+3192x^159+3222x^160+2844x^161+1728x^162+4260x^163+4323x^164+3636x^165+2076x^166+5004x^167+4731x^168+3348x^169+2100x^170+4488x^171+3126x^172+1980x^173+948x^174+1632x^175+957x^176+708x^177+216x^178+276x^179+111x^180+60x^181+60x^184+21x^188+12x^192+9x^196+6x^200+6x^204

The gray image is a linear code over GF(4) with n=220, k=8 and d=148.
This code was found by Heurico 1.16 in 15.6 seconds.