The generator matrix

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

generates a code of length 53 over F4[X]/(X^2) who´s minimum homogenous weight is 145.

Homogenous weight enumerator: w(x)=1x^0+648x^145+1188x^146+444x^147+81x^148+2688x^149+3012x^150+1188x^151+150x^152+4356x^153+4716x^154+1920x^155+267x^156+5556x^157+6108x^158+1992x^159+195x^160+6372x^161+6180x^162+2112x^163+141x^164+5244x^165+4500x^166+1176x^167+144x^168+2496x^169+1740x^170+372x^171+33x^172+288x^173+204x^174+12x^175+6x^180+6x^184

The gray image is a linear code over GF(4) with n=212, k=8 and d=145.
This code was found by Heurico 1.16 in 817 seconds.