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+2X+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 0.016 seconds.