The generator matrix

 1  0  0  0  1  1  1  X  1 a^2*X  1  1  1  1  1  X  1  1  0  X  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1 a^2*X a*X  1  1  1  1  1  1  1  1  1  1
 0  1  0  0  X  1 X+1  1 a*X  1 a^2*X+a X+a^2 a^2 a*X+1 a^2*X+1  1 X+a  a  1  1 a^2*X  1  1  1 X+a^2  0 a*X a^2*X+a^2 X+a^2  a  X a^2 a*X+1 a^2*X+1 a^2*X  0  1 a^2  0  1 a^2*X+a X+a a*X a^2*X+1 a^2*X+1 a^2*X+a^2 a*X+1
 0  0  1  0 a^2*X+1  1 a^2*X a^2*X+1 X+1 a^2*X+a a^2*X+a^2  X a^2*X+a^2 X+a a^2 a^2*X+a  0 a^2*X+a a*X  1 a^2 a*X+1  a X+a X+a a*X+1 a^2*X X+1 a*X+a X+1 X+a^2 X+1 a^2*X a^2*X+a^2 a*X+a  1 a*X+a^2  0 a^2*X+a^2 a^2  1 a*X+a a*X  a a^2*X+a a^2*X+a a*X
 0  0  0  1 a^2  X a*X+a^2 a*X+a^2  a a^2*X X+a a^2*X+a^2 a^2*X+1 a*X+1 a*X+a^2 a^2*X+a X+1 a*X a*X+1 a*X+a a^2*X+a^2  1  1 a^2*X+a^2 a*X+a^2 a*X+1  1 X+1 X+a X+a a^2*X+a a*X+a^2  0  0  1 a^2*X+1  1 a^2*X X+1  a a*X+1 a^2 a^2*X+a^2 a*X+1 a^2*X+a a^2*X+a^2  X

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

Homogenous weight enumerator: w(x)=1x^0+288x^127+747x^128+744x^129+1068x^130+1584x^131+1977x^132+1536x^133+2436x^134+2508x^135+3279x^136+2556x^137+2952x^138+3636x^139+4419x^140+3360x^141+3828x^142+4128x^143+4887x^144+3648x^145+3192x^146+3552x^147+3006x^148+1728x^149+1656x^150+1044x^151+1101x^152+252x^153+228x^154+156x^155+27x^156+9x^160+3x^164

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 12.2 seconds.