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

generates a code of length 55 over F4[X]/(X^2) who´s minimum homogenous weight is 154.

Homogenous weight enumerator: w(x)=1x^0+648x^154+504x^155+165x^156+1440x^158+1392x^159+210x^160+2256x^162+1452x^163+213x^164+1908x^166+1092x^167+228x^168+1548x^170+900x^171+96x^172+1020x^174+636x^175+54x^176+396x^178+168x^179+48x^180+3x^188+3x^192+3x^196

The gray image is a linear code over GF(4) with n=220, k=7 and d=154.
This code was found by Heurico 1.16 in 16.1 seconds.