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

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+984x^142+948x^143+198x^144+3228x^146+2664x^147+597x^148+5568x^150+4344x^151+861x^152+7752x^154+5436x^155+828x^156+9096x^158+5556x^159+834x^160+6780x^162+3888x^163+516x^164+3072x^166+1632x^167+231x^168+384x^170+108x^171+24x^172+3x^176+3x^180

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 30.1 seconds.