The generator matrix

 1  0  0  0  1  1  1  1  2  1  1 X+2  1  X  X  2  1  1  0  1  1  1  1  0  1 X+2  1  1  X  2  X  1  1  0  1  1  1  1  1  1  2  0  1
 0  1  0  0  0  2  3  1  1  0  3  1  3  2  1  1 X+2  X X+2  1  2 X+1  3  1 X+3  2 X+3 X+1  1  X  1  3  2  X  1  X  1  2 X+2 X+2  1  1 X+1
 0  0  1  0  2  1  2  3  1  3  X X+2  1  1 X+3 X+3 X+2  3  1 X+3 X+2  X X+2  X X+1  0  2  1  3  1  1  X X+3  1  0  X X+3 X+2  2  1 X+3  3  1
 0  0  0  1 X+3 X+3 X+1  2  3 X+2  X  1  1  3  2  1  3 X+3  1  X  2  0 X+3 X+2  X  1 X+2  1 X+1  0  X  0  0 X+2  3 X+3 X+1 X+2  1  X X+2  X  2

generates a code of length 43 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+378x^38+872x^40+950x^42+800x^44+574x^46+381x^48+106x^50+24x^52+8x^54+2x^56

The gray image is a code over GF(2) with n=172, k=12 and d=76.
This code was found by Heurico 1.16 in 6.98 seconds.