The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+69x^22+426x^23+1003x^24+1990x^25+3061x^26+5440x^27+6917x^28+8832x^29+9500x^30+9422x^31+7136x^32+5390x^33+3132x^34+1828x^35+795x^36+420x^37+105x^38+36x^39+20x^40+8x^41+3x^42+2x^46

The gray image is a code over GF(2) with n=120, k=16 and d=44.
This code was found by Heurico 1.13 in 20.5 seconds.