The generator matrix

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

generates a code of length 55 over F4[X]/(X^2) who´s minimum homogenous weight is 158.

Homogenous weight enumerator: w(x)=1x^0+516x^158+528x^159+99x^160+636x^162+372x^163+54x^164+516x^166+252x^167+36x^168+324x^170+180x^171+36x^172+168x^174+132x^175+24x^176+144x^178+72x^179+6x^180

The gray image is a linear code over GF(4) with n=220, k=6 and d=158.
This code was found by Heurico 1.16 in 0.063 seconds.