The generator matrix

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

generates a code of length 43 over F4[X]/(X^2) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+216x^114+480x^115+360x^116+264x^117+1392x^118+2076x^119+765x^120+876x^121+2652x^122+4080x^123+1113x^124+1824x^125+4200x^126+6228x^127+1662x^128+2760x^129+6000x^130+7728x^131+1776x^132+2616x^133+5088x^134+5460x^135+1020x^136+876x^137+1788x^138+1536x^139+333x^140+168x^142+60x^143+42x^144+45x^148+27x^152+18x^156+3x^160+3x^164

The gray image is a linear code over GF(4) with n=172, k=8 and d=114.
This code was found by Heurico 1.16 in 93.5 seconds.