The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  1  0  1 3X+2  1  1  1  1  2  1  1  1  1 3X+2  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 3X+2 X+1  1 2X+3  1  2 3X+2 X+3 2X+3  1 3X 3X 2X+1 2X+1  1  0
 0  0 2X  0  0  0  0 2X  0 2X 2X 2X  0 2X  0  0 2X 2X  0  0 2X  0 2X 2X  0  0  0 2X  0
 0  0  0 2X  0  0 2X 2X  0 2X  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0  0  0  0 2X 2X  0  0
 0  0  0  0 2X  0 2X  0 2X 2X 2X 2X  0  0 2X  0 2X  0  0 2X 2X 2X  0  0  0  0 2X  0  0
 0  0  0  0  0 2X  0 2X 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0 2X  0  0 2X 2X  0  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+32x^24+84x^25+308x^26+496x^27+688x^28+888x^29+690x^30+496x^31+297x^32+84x^33+20x^34+4x^36+2x^38+2x^40+4x^42

The gray image is a code over GF(2) with n=232, k=12 and d=96.
This code was found by Heurico 1.16 in 0.094 seconds.