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.