The generator matrix

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

generates a code of length 53 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+126x^144+24x^146+288x^147+576x^148+240x^150+864x^151+942x^152+432x^154+1116x^155+1482x^156+1056x^158+1296x^159+1680x^160+888x^162+1608x^163+1473x^164+432x^166+816x^167+657x^168+156x^171+96x^172+30x^176+39x^180+27x^184+24x^188+9x^192+6x^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 1.16 seconds.