The generator matrix

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

generates a code of length 47 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 127.

Homogenous weight enumerator: w(x)=1x^0+516x^127+444x^128+552x^129+1092x^130+2328x^131+1323x^132+1512x^133+2100x^134+3948x^135+2157x^136+2292x^137+2928x^138+4836x^139+3357x^140+3036x^141+4332x^142+6000x^143+3333x^144+3084x^145+3480x^146+4644x^147+2049x^148+1548x^149+1200x^150+2064x^151+549x^152+264x^153+228x^154+240x^155+87x^156+6x^160+6x^168

The gray image is a linear code over GF(4) with n=188, k=8 and d=127.
This code was found by Heurico 1.16 in 12.5 seconds.