The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+130x^38+32x^39+232x^40+56x^41+272x^42+176x^43+341x^44+128x^45+261x^46+112x^47+140x^48+8x^49+81x^50+46x^52+21x^54+7x^56+3x^58+1x^68

The gray image is a code over GF(2) with n=176, k=11 and d=76.
This code was found by Heurico 1.16 in 0.281 seconds.