The generator matrix

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

generates a code of length 54 over F4[X]/(X^2) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+72x^146+300x^147+828x^148+288x^149+1176x^150+1488x^151+1953x^152+648x^153+1932x^154+2388x^155+2949x^156+1008x^157+3684x^158+3708x^159+4917x^160+1320x^161+4044x^162+4188x^163+5673x^164+1440x^165+4416x^166+3672x^167+4284x^168+1080x^169+2436x^170+2220x^171+1572x^172+336x^173+612x^174+444x^175+228x^176+24x^177+60x^178+24x^179+42x^180+42x^184+18x^188+12x^192+3x^196+3x^200+3x^204

The gray image is a linear code over GF(4) with n=216, k=8 and d=146.
This code was found by Heurico 1.16 in 46.7 seconds.