The generator matrix

 1  0  0  0  1  1  1  X  1 X^2  1 X^2+X  1  X  1  1  1  1  0  2 X^2 X^2+X  1  1 X+2  1  1  1  1
 0  1  0  0  2  X X^2+X+2  X X^2+1  1 X+1  1  1  1 X+3 X+3 X^2+X+2  3 X^2+2  1 X^2+X  1 X+3 X^2+2  1  1 X^2+X  2  0
 0  0  1  0  3  2  1  1 X^2+X+1 X^2+3 X^2+X  3  X X^2+X X^2+3 X+3 X^2+X+2 X^2+2  1 X^2  1 X^2+1 X+2 X^2 X^2+2 X^2+X+1 X+3 X^2+1 X^2+X+2
 0  0  0  1  1  3  2 X+3  X X^2+X+1 X+3 X^2  2 X^2+X+3 X^2+1  X X^2+X  2 X+1 X^2+X+2 X^2 X^2+1 X^2+X+2 X^2+X+1 X^2+X+3  1 X^2+X+1 X+1  X

generates a code of length 29 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+307x^24+1880x^25+4097x^26+7748x^27+11934x^28+13390x^29+12204x^30+8146x^31+3798x^32+1460x^33+401x^34+136x^35+24x^36+6x^37+2x^38+2x^39

The gray image is a code over GF(2) with n=232, k=16 and d=96.
This code was found by Heurico 1.16 in 13.4 seconds.