The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+44x^39+187x^40+124x^41+187x^42+108x^43+128x^44+46x^45+63x^46+32x^47+39x^48+20x^49+21x^50+8x^51+12x^52+2x^53+1x^54+1x^56

The gray image is a code over GF(2) with n=172, k=10 and d=78.
This code was found by Heurico 1.11 in 0.0358 seconds.