The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+74x^38+244x^39+271x^40+394x^41+752x^42+712x^43+782x^44+342x^45+199x^46+164x^47+58x^48+46x^49+30x^50+16x^51+8x^52+2x^53+1x^70

The gray image is a code over GF(2) with n=344, k=12 and d=152.
This code was found by Heurico 1.16 in 0.219 seconds.