The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1  1  0  1  1  1  1  1  1  1 X+2  1  1 X+2  X  0  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  1  0  3  1 X+2 X+1  1 X+1  3  1  0 X+2  1  0 X+2 X+1  1  3  3  3 X+1  0 X+3  3  1  0 X+2  1  2  1 X+1
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  2  2  2  0  0  2  0  2  2  2  2  2  2  0  2  0  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  2  0  2  0  0  2  2  2  2  0  2  2  2  0  2  0  2  2  0  0  0  2  0  2  2  0  0  2
 0  0  0  0  2  0  0  0  0  0  0  2  2  0  2  2  2  2  2  0  2  0  0  2  0  2  2  2  2  0  2  2  0  2  2  2  0  2  2  2  0  2  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  0  0  2  2  2  0  2  2  0  0  2  0  2  0  0  0  2  2  0  2  0  0  2  0  0  0  2  0
 0  0  0  0  0  0  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  0  0  0  2  2  2  2  0  0  0  2  0  2  2  0  0  0  0  2  2  2  2
 0  0  0  0  0  0  0  2  0  2  0  0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  2  2  0  2  0  0  2  2  0  2  0  0  2  0  2
 0  0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  2  2  0  2  0  2  0  2  2  2  2  2  2  2  2  0  0  0  0  2  2  0  2  0  2  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+51x^34+18x^35+106x^36+222x^37+217x^38+588x^39+482x^40+1028x^41+700x^42+1360x^43+694x^44+1120x^45+466x^46+564x^47+206x^48+188x^49+75x^50+30x^51+30x^52+2x^53+21x^54+14x^56+6x^58+2x^60+1x^64

The gray image is a code over GF(2) with n=172, k=13 and d=68.
This code was found by Heurico 1.16 in 2.31 seconds.