The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+310x^39+211x^40+672x^41+236x^42+602x^43+208x^44+676x^45+155x^46+460x^47+142x^48+208x^49+50x^50+114x^51+14x^52+28x^53+7x^54+2x^55

The gray image is a code over GF(2) with n=176, k=12 and d=78.
This code was found by Heurico 1.11 in 3.84 seconds.