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  1  1  1  1  X  1  1  1  1 a^2*X  1  1  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 X+1 a*X+1 a*X+a  0  1 a*X+1  X a*X+a  0  1 a^2*X a*X+a^2  1 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^2*X a^2*X X+1  X a*X+1 X+1 a*X+a^2 a^2*X+a a*X+a^2 a*X+a X+1 X+a^2 a^2*X+1 a^2*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*X a^2*X  0  X a^2*X a*X  X a*X a^2*X a^2*X  0 a^2*X a*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+396x^154+588x^155+780x^156+732x^158+1296x^159+1356x^160+948x^162+1296x^163+1176x^164+900x^166+1200x^167+969x^168+960x^170+1116x^171+774x^172+528x^174+480x^175+471x^176+144x^178+168x^179+96x^180+3x^184+6x^188

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 25.5 seconds.