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

generates a code of length 51 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 139.

Homogenous weight enumerator: w(x)=1x^0+228x^139+138x^140+72x^141+204x^142+828x^143+195x^144+324x^145+336x^146+1368x^147+162x^148+624x^149+648x^150+2004x^151+147x^152+840x^153+912x^154+2196x^155+117x^156+936x^157+780x^158+1764x^159+66x^160+276x^161+192x^162+720x^163+54x^164+108x^167+42x^168+21x^172+24x^176+30x^180+21x^184+6x^188

The gray image is a linear code over GF(4) with n=204, k=7 and d=139.
This code was found by Heurico 1.16 in 3.81 seconds.