The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  X  1  2  1  2  X  1  1
 0 2X+2  0 2X+2  0 2X+2  0  2 2X 2X+2  0  0 2X+2 2X+2  2  0 2X 2X+2  2 2X  0 2X+2 2X 2X+2 2X+2 2X+2 2X+2  2  0
 0  0 2X  0  0  0  0  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X 2X  0  0 2X  0  0 2X  0 2X 2X
 0  0  0 2X  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X 2X  0  0
 0  0  0  0 2X  0  0  0  0 2X 2X  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X  0 2X 2X  0  0  0
 0  0  0  0  0 2X  0 2X  0 2X 2X 2X  0 2X  0 2X  0  0  0  0  0 2X 2X 2X  0  0  0 2X 2X
 0  0  0  0  0  0 2X  0 2X  0 2X  0 2X  0 2X 2X 2X 2X  0 2X 2X  0 2X  0  0  0  0 2X  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+90x^24+112x^26+192x^27+193x^28+896x^29+160x^30+192x^31+144x^32+48x^34+14x^36+4x^40+1x^44+1x^48

The gray image is a code over GF(2) with n=232, k=11 and d=96.
This code was found by Heurico 1.16 in 0.047 seconds.