The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  0  1
 0  X  0  0  0  0  0  0  2  2  X X+2  X X+2  0 X+2  X  2  X  2 X+2 X+2  2  2  2  0  0  2  0  X
 0  0  X  0  0  0  0  0  0  0  0  0  2  2 X+2 X+2  X  X X+2  X  2  X  X  2  X  X  X  2  0  X
 0  0  0  X  0  0  2 X+2  X  X  X  X X+2  2 X+2  X  2  0  0  0  2  0 X+2  0  2 X+2 X+2  X  X  0
 0  0  0  0  X  0 X+2 X+2  X  2 X+2 X+2  0  X  2  X  X  X X+2 X+2  0  2  X X+2 X+2  X  2  2  2  0
 0  0  0  0  0  X  X  2 X+2  X X+2  2  2 X+2  0  0  2  0 X+2 X+2  X  2  2  X X+2 X+2 X+2 X+2  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+43x^22+124x^23+193x^24+196x^25+267x^26+388x^27+717x^28+1332x^29+1667x^30+1364x^31+710x^32+364x^33+273x^34+220x^35+159x^36+92x^37+53x^38+16x^39+12x^40+1x^54

The gray image is a code over GF(2) with n=120, k=13 and d=44.
This code was found by Heurico 1.16 in 1.82 seconds.