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

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+504x^139+843x^140+516x^141+1164x^142+2064x^143+2154x^144+1188x^145+1920x^146+3336x^147+3912x^148+1548x^149+2904x^150+4236x^151+4530x^152+2376x^153+3048x^154+5148x^155+4614x^156+1968x^157+3012x^158+4236x^159+3564x^160+1368x^161+1560x^162+1812x^163+1212x^164+240x^165+216x^166+168x^167+156x^168+12x^169+3x^172+3x^176

The gray image is a linear code over GF(4) with n=204, k=8 and d=139.
This code was found by Heurico 1.16 in 18.6 seconds.