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

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+564x^145+1308x^146+468x^147+549x^148+2220x^149+2916x^150+984x^151+1065x^152+3540x^153+4656x^154+1344x^155+1497x^156+4740x^157+6168x^158+1836x^159+1665x^160+5184x^161+6108x^162+1704x^163+1434x^164+4584x^165+4404x^166+1044x^167+804x^168+1992x^169+1944x^170+276x^171+141x^172+216x^173+144x^174+24x^175+6x^176+3x^180+3x^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 58.4 seconds.