The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+63x^32+40x^34+278x^36+220x^38+64x^39+829x^40+320x^41+928x^42+640x^43+1392x^44+640x^45+1064x^46+320x^47+709x^48+64x^49+280x^50+206x^52+28x^54+91x^56+12x^60+3x^64

The gray image is a code over GF(2) with n=176, k=13 and d=64.
This code was found by Heurico 1.16 in 3.42 seconds.