The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+200x^21+816x^22+1700x^23+3697x^24+6162x^25+10448x^26+14242x^27+18788x^28+18804x^29+18676x^30+14438x^31+10901x^32+6084x^33+3512x^34+1598x^35+652x^36+236x^37+84x^38+22x^39+9x^40+2x^41

The gray image is a code over GF(2) with n=116, k=17 and d=42.
This code was found by Heurico 1.13 in 71.8 seconds.