The generator matrix

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

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+388x^38+884x^40+892x^42+811x^44+638x^46+322x^48+128x^50+29x^52+2x^54+1x^56

The gray image is a code over GF(2) with n=172, k=12 and d=76.
This code was found by Heurico 1.11 in 1.23 seconds.