The generator matrix

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

generates a code of length 43 over F4[X]/(X^2) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+339x^116+60x^117+156x^119+1125x^120+312x^121+336x^123+1515x^124+696x^125+936x^127+2610x^128+816x^129+1104x^131+2691x^132+876x^133+540x^135+1518x^136+312x^137+279x^140+66x^144+54x^148+21x^152+18x^156+3x^160

The gray image is a linear code over GF(4) with n=172, k=7 and d=116.
This code was found by Heurico 1.16 in 6.59 seconds.