The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+72x^21+410x^22+930x^23+2249x^24+3716x^25+6885x^26+9398x^27+15202x^28+16726x^29+20001x^30+16222x^31+15339x^32+9782x^33+7150x^34+3678x^35+1910x^36+794x^37+428x^38+104x^39+51x^40+14x^41+5x^42+4x^43+1x^46

The gray image is a code over GF(2) with n=120, k=17 and d=42.
This code was found by Heurico 1.13 in 105 seconds.