The generator matrix

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

generates a code of length 47 over F4[X]/(X^2) who´s minimum homogenous weight is 128.

Homogenous weight enumerator: w(x)=1x^0+357x^128+132x^129+168x^130+756x^132+660x^133+432x^134+1275x^136+1224x^137+576x^138+1461x^140+1800x^141+912x^142+1740x^144+1716x^145+792x^146+1137x^148+612x^149+192x^150+285x^152+63x^156+33x^160+39x^164+12x^168+9x^176

The gray image is a linear code over GF(4) with n=188, k=7 and d=128.
This code was found by Heurico 1.16 in 64.4 seconds.