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

generates a code of length 53 over F4[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+381x^144+1008x^145+324x^146+192x^147+1443x^148+2928x^149+852x^150+408x^151+2871x^152+5004x^153+1524x^154+492x^155+3636x^156+7056x^157+2280x^158+624x^159+4359x^160+8232x^161+2316x^162+888x^163+3948x^164+6576x^165+1572x^166+408x^167+2271x^168+2556x^169+348x^170+60x^171+432x^172+432x^173+36x^176+27x^180+30x^184+12x^188+3x^192+6x^196

The gray image is a linear code over GF(4) with n=212, k=8 and d=144.
This code was found by Heurico 1.16 in 69.6 seconds.