The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  0  1  1  1 X+2  1  1 X+2  1  1  1  X  1  0  1  0  1  1  2  1  1  1  1  X  1 X+2  X  1  1  1  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0  1 X+1 X+2  3  1  0  3  1 X+2  0  3  1 X+1  1 X+1  1 X+2 X+3  1  2  X  3  2  0  2  1  0  2  2  0 X+2
 0  0  2  0  0  0  0  0  0  2  2  0  2  0  0  0  2  2  2  2  2  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  2  0  0  0  0
 0  0  0  2  0  0  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  2  2  0  0  2  2  0  0  2  2  0  0  2  0  0  2  2  0  2  2
 0  0  0  0  2  0  0  0  2  0  2  0  2  2  2  2  2  0  2  0  2  0  2  0  2  2  0  2  0  0  2  0  0  2  0  2  2  2  2  0  0  0  0  0
 0  0  0  0  0  2  0  2  2  0  2  0  2  0  2  2  0  2  0  2  0  2  0  0  2  2  0  2  0  2  0  2  2  2  2  0  2  2  0  2  0  2  2  2
 0  0  0  0  0  0  2  2  0  2  0  2  2  2  2  2  2  2  2  0  0  2  0  0  0  2  0  0  2  0  0  0  2  0  2  0  2  2  2  0  2  2  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+44x^38+72x^39+235x^40+76x^41+348x^42+120x^43+324x^44+108x^45+336x^46+56x^47+177x^48+68x^49+34x^50+8x^51+26x^52+4x^53+2x^54+3x^56+2x^58+2x^60+2x^62

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 0.166 seconds.