The generator matrix

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

generates a code of length 55 over F4[X]/(X^2) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+312x^150+660x^151+234x^152+732x^153+1716x^154+2412x^155+789x^156+1656x^157+3168x^158+3792x^159+1392x^160+2292x^161+4056x^162+4632x^163+1572x^164+2760x^165+4812x^166+6108x^167+1533x^168+2508x^169+4188x^170+4452x^171+1044x^172+1776x^173+2640x^174+2208x^175+543x^176+516x^177+504x^178+312x^179+48x^180+48x^181+108x^182+9x^184+3x^188

The gray image is a linear code over GF(4) with n=220, k=8 and d=150.
This code was found by Heurico 1.16 in 14.6 seconds.