The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+64x^15+160x^16+306x^17+552x^18+1068x^19+1794x^20+2624x^21+3130x^22+2698x^23+1866x^24+1116x^25+582x^26+250x^27+78x^28+48x^29+22x^30+14x^31+5x^32+2x^33+2x^34+2x^35

The gray image is a code over GF(2) with n=88, k=14 and d=30.
This code was found by Heurico 1.16 in 2.85 seconds.