The generator matrix

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

generates a code of length 47 over F4[X]/(X^2) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+60x^124+84x^125+72x^126+420x^127+768x^128+684x^129+480x^130+1800x^131+1848x^132+1728x^133+1296x^134+3024x^135+3528x^136+2784x^137+1884x^138+4812x^139+4392x^140+4260x^141+2520x^142+5844x^143+4545x^144+3420x^145+2088x^146+4080x^147+3177x^148+1992x^149+816x^150+1464x^151+945x^152+408x^153+60x^154+60x^155+93x^156+60x^160+27x^164+3x^168+3x^172+6x^176

The gray image is a linear code over GF(4) with n=188, k=8 and d=124.
This code was found by Heurico 1.16 in 12.9 seconds.