The generator matrix

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

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+216x^37+488x^38+762x^39+1192x^40+1368x^41+1503x^42+1752x^43+1825x^44+1820x^45+1639x^46+1376x^47+1038x^48+624x^49+389x^50+192x^51+99x^52+68x^53+13x^54+14x^55+5x^56

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 8.42 seconds.