The generator matrix

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

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+61x^22+150x^23+313x^24+494x^25+823x^26+1268x^27+1759x^28+2160x^29+2289x^30+2228x^31+1730x^32+1256x^33+869x^34+500x^35+277x^36+120x^37+54x^38+14x^39+15x^40+2x^41+1x^56

The gray image is a code over GF(2) with n=120, k=14 and d=44.
This code was found by Heurico 1.16 in 4.72 seconds.