The generator matrix

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

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+105x^144+84x^145+240x^147+408x^148+480x^149+732x^151+669x^152+924x^153+1140x^155+633x^156+1296x^157+1608x^159+879x^160+1788x^161+1608x^163+747x^164+1296x^165+732x^167+402x^168+276x^169+84x^171+129x^172+36x^176+24x^180+27x^184+24x^188+9x^192+3x^196

The gray image is a linear code over GF(4) with n=212, k=7 and d=144.
This code was found by Heurico 1.16 in 1.14 seconds.