The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+144x^37+597x^38+726x^39+1203x^40+1292x^41+1773x^42+1440x^43+2138x^44+1518x^45+1739x^46+1174x^47+1186x^48+658x^49+457x^50+174x^51+109x^52+34x^53+8x^54+4x^55+2x^56+2x^57+2x^58+2x^59+1x^60

The gray image is a code over GF(2) with n=176, k=14 and d=74.
This code was found by Heurico 1.16 in 7.26 seconds.