The generator matrix

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

generates a code of length 54 over F4[X]/(X^2) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+240x^147+402x^148+552x^149+828x^150+1968x^151+1455x^152+1668x^153+1656x^154+3456x^155+2013x^156+2424x^157+2700x^158+4044x^159+3192x^160+2784x^161+3156x^162+5304x^163+3636x^164+3012x^165+3036x^166+4692x^167+2757x^168+2352x^169+1944x^170+2652x^171+1149x^172+972x^173+444x^174+672x^175+234x^176+60x^177+60x^178+12x^179+6x^184+3x^192

The gray image is a linear code over GF(4) with n=216, k=8 and d=147.
This code was found by Heurico 1.16 in 15.1 seconds.