The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  1  1  X aX  1  1  1  1  1  1  X aX  1  1  1  1  1  1  1  1  0  1  0  1  1  1 aX  1  1  X  1  1  1  1  1  X  1  1  1  1  1
 0  1  0  0  X aX  X (a+1)X (a+1)X (a+1)X+1  a  1 aX+a  1  1 a+1 (a+1)X+a+1  a X+a+1 aX aX+1  1  1 aX+a aX X+a+1 (a+1)X  a (a+1)X+a (a+1)X+a aX+1  1  1  1 (a+1)X+a X+a  0  1 X+a+1 X+1  1 aX+a+1 aX aX+1  1 aX+1  1 X+a  0 X+1  0  0
 0  0  1  0 (a+1)X+1 (a+1)X  a (a+1)X  0 a+1 X+a+1 X+1 (a+1)X+a X+1 (a+1)X+a X+a (a+1)X+1  1 aX+1 X+1  X  a (a+1)X  0 (a+1)X+a X+a a+1 aX+a aX+1 (a+1)X+a+1 X+a+1  a aX aX+1 aX X+1 aX+1  0  X (a+1)X aX+1 a+1 a+1  a (a+1)X+a+1 aX+a (a+1)X+a+1 (a+1)X+a a+1 aX+1 aX+a+1 (a+1)X+a
 0  0  0  1 a+1  1 X+a+1  a aX+a+1 (a+1)X+a+1 (a+1)X+a+1 (a+1)X+a X+1 aX+a X+a (a+1)X  1 aX+a aX+a X+a aX+a+1  1 X+a+1 aX aX+1 (a+1)X+a X+a X+a+1 aX+1 (a+1)X+a X+a X+a+1 X+1 (a+1)X  1 aX+a+1 (a+1)X+1 (a+1)X+a X+a+1 X+a (a+1)X+1 a+1 (a+1)X+1  1  X (a+1)X+a (a+1)X+a X+a+1 X+1  1 aX+a a+1

generates a code of length 52 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 142.

Homogenous weight enumerator: w(x)=1x^0+912x^142+984x^143+183x^144+3408x^146+2628x^147+522x^148+5616x^150+4284x^151+876x^152+7620x^154+5508x^155+924x^156+8760x^158+5568x^159+885x^160+7200x^162+3996x^163+552x^164+2952x^166+1356x^167+126x^168+396x^170+252x^171+12x^172+3x^176+6x^180+6x^184

The gray image is a linear code over GF(4) with n=208, k=8 and d=142.
This code was found by Heurico 1.16 in 21.3 seconds.