The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+174x^34+510x^35+917x^36+1904x^37+2528x^38+4170x^39+4845x^40+6614x^41+6794x^42+8200x^43+6966x^44+6990x^45+5070x^46+4272x^47+2388x^48+1586x^49+786x^50+442x^51+204x^52+122x^53+38x^54+6x^55+6x^56+2x^58+1x^60

The gray image is a code over GF(2) with n=172, k=16 and d=68.
This code was found by Heurico 1.13 in 35 seconds.