The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  1  1  1  2  1  1  1 2X 2X  1  1  1
 0 2X+2  0  0  0  2 2X+2  2  0 2X 2X+2 2X+2  0 2X+2 2X  2 2X  0  2  0  2  0 2X  2 2X  2  2  0 2X
 0  0 2X+2  0  2  2  2 2X  0 2X  2 2X+2  2  2 2X+2  0  0  2 2X 2X+2 2X  2  2  2  2 2X+2  0 2X+2 2X+2
 0  0  0 2X+2  2 2X 2X+2 2X+2  0 2X+2 2X 2X+2  2  2  2 2X+2  2 2X 2X  2  2 2X+2  0 2X+2  2 2X  2 2X 2X+2
 0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X  0  0 2X  0 2X  0  0 2X 2X

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+33x^24+60x^25+92x^26+310x^27+142x^28+826x^29+132x^30+294x^31+70x^32+16x^33+26x^34+18x^35+8x^36+10x^37+5x^38+2x^39+2x^40+1x^46

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 0.063 seconds.