The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+148x^34+464x^35+1109x^36+2114x^37+3139x^38+5486x^39+7469x^40+10332x^41+12212x^42+15060x^43+15127x^44+15588x^45+12602x^46+10932x^47+7346x^48+5320x^49+3194x^50+1688x^51+876x^52+490x^53+215x^54+94x^55+40x^56+12x^57+10x^58+4x^59

The gray image is a code over GF(2) with n=176, k=17 and d=68.
This code was found by Heurico 1.13 in 130 seconds.