The generator matrix

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

generates a code of length 43 over F4[X]/(X^2) who´s minimum homogenous weight is 119.

Homogenous weight enumerator: w(x)=1x^0+840x^119+561x^120+2412x^123+765x^124+2904x^127+1041x^128+2976x^131+840x^132+2208x^135+606x^136+948x^139+261x^140+9x^144+6x^148+3x^152+3x^160

The gray image is a linear code over GF(4) with n=172, k=7 and d=119.
This code was found by Heurico 1.16 in 672 seconds.