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

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+588x^127+420x^128+648x^129+792x^130+1992x^131+1809x^132+1548x^133+1968x^134+3888x^135+2835x^136+2148x^137+2352x^138+5220x^139+3819x^140+3000x^141+3060x^142+6132x^143+3966x^144+2976x^145+2796x^146+4776x^147+2787x^148+1692x^149+1164x^150+1680x^151+702x^152+276x^153+156x^154+300x^155+33x^156+9x^160+3x^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 13.5 seconds.