The generator matrix

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

generates a code of length 53 over F4[X]/(X^2) who´s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+261x^148+804x^149+300x^150+84x^151+924x^152+1764x^153+564x^154+216x^155+1074x^156+1848x^157+564x^158+192x^159+957x^160+1692x^161+324x^162+168x^163+930x^164+1416x^165+288x^166+108x^167+576x^168+624x^169+216x^170+126x^172+300x^173+48x^174+6x^176+9x^180

The gray image is a linear code over GF(4) with n=212, k=7 and d=148.
This code was found by Heurico 1.16 in 0.936 seconds.