The generator matrix

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

generates a code of length 51 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 142.

Homogenous weight enumerator: w(x)=1x^0+444x^142+504x^143+150x^144+1716x^146+1368x^147+270x^148+2124x^150+1224x^151+168x^152+1944x^154+1356x^155+210x^156+1716x^158+1044x^159+105x^160+948x^162+588x^163+66x^164+324x^166+60x^167+42x^168+6x^172+3x^176+3x^192

The gray image is a linear code over GF(4) with n=204, k=7 and d=142.
This code was found by Heurico 1.16 in 0.71 seconds.