The generator matrix

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

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+140x^38+112x^39+279x^40+200x^41+258x^42+176x^43+247x^44+160x^45+205x^46+96x^47+90x^48+24x^49+33x^50+13x^52+3x^54+10x^56+1x^58

The gray image is a code over GF(2) with n=172, k=11 and d=76.
This code was found by Heurico 1.16 in 0.166 seconds.