The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X X 1 1 1 1 1 1 1 1
0 2X 0 0 0 0 0 2X 0 0 0 0 2X 2X 0 2X 0 2X 2X 0 2X 0 2X 2X 0 0 0 2X 2X
0 0 2X 0 0 0 0 2X 0 0 2X 2X 2X 2X 2X 0 2X 2X 2X 2X 2X 0 2X 0 2X 0 2X 2X 0
0 0 0 2X 0 0 0 2X 0 2X 2X 0 0 0 2X 2X 2X 0 2X 0 2X 0 0 0 2X 2X 2X 2X 2X
0 0 0 0 2X 0 0 2X 0 2X 0 2X 0 2X 0 0 2X 2X 2X 0 0 2X 0 2X 2X 0 2X 2X 2X
0 0 0 0 0 2X 0 2X 2X 0 0 2X 0 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 2X 0 2X 0 2X
0 0 0 0 0 0 2X 2X 2X 0 2X 0 0 2X 0 2X 2X 2X 0 2X 0 0 2X 0 0 2X 2X 0 0
generates a code of length 29 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+38x^24+136x^28+768x^29+57x^32+23x^36+1x^52
The gray image is a code over GF(2) with n=232, k=10 and d=96.
This code was found by Heurico 1.16 in 0.031 seconds.