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 1 1 1 1 X X 1 1 1 1 1 X 1 1 1 X 1 X 1 1
0 2X 0 0 0 0 0 0 0 0 2X 2X 0 0 0 2X 0 0 0 0 2X 2X 2X 2X 0 2X 2X 2X 2X 0 2X 2X 0 2X 2X 2X 0 2X 0 0 2X 2X 0
0 0 2X 0 0 0 0 0 0 2X 2X 2X 0 2X 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 0 0 0 0 0 0 2X 2X 2X 0 2X 2X 2X 0 2X 0 0
0 0 0 2X 0 0 0 0 0 2X 0 2X 2X 2X 0 2X 0 2X 2X 0 0 0 0 0 2X 0 2X 2X 0 2X 0 2X 2X 0 2X 0 0 2X 0 2X 0 2X 0
0 0 0 0 2X 0 0 0 2X 0 0 2X 2X 0 2X 2X 0 0 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 0 2X 0 0 2X 2X 0 0
0 0 0 0 0 2X 0 0 2X 0 2X 0 0 2X 2X 2X 0 2X 2X 0 0 0 0 2X 2X 0 0 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 2X 2X 0 0 2X
0 0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 2X 2X 2X 0 0 2X 0 0 2X 0 2X 0 2X 2X 0 2X 2X 0 0 0 0 2X 0 2X 2X 2X 2X 2X 0
0 0 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 2X 0 2X 0 2X 0 0 2X 2X 0 0 0 2X 2X 0 0 0 2X 0 2X 2X 0 2X 0 2X 2X 2X 2X 0
generates a code of length 43 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+63x^36+8x^38+106x^40+80x^42+1536x^43+117x^44+40x^46+61x^48+27x^52+8x^56+1x^76
The gray image is a code over GF(2) with n=344, k=11 and d=144.
This code was found by Heurico 1.16 in 0.125 seconds.