The generator matrix

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

generates a code of length 43 over F4[X]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+264x^112+768x^113+840x^114+1284x^115+1656x^116+3960x^117+3432x^118+4164x^119+4512x^120+8544x^121+7116x^122+8424x^123+8772x^124+15828x^125+13476x^126+14964x^127+13434x^128+23136x^129+16848x^130+17460x^131+14214x^132+21408x^133+14016x^134+11724x^135+8511x^136+10656x^137+5148x^138+3264x^139+1761x^140+1716x^141+564x^142+156x^143+48x^144+30x^148+27x^152+9x^156+3x^160+6x^164

The gray image is a linear code over GF(4) with n=172, k=9 and d=112.
This code was found by Heurico 1.16 in 144 seconds.