The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+49x^16+64x^17+234x^18+364x^19+828x^20+1182x^21+1726x^22+2436x^23+2449x^24+2534x^25+1886x^26+1252x^27+754x^28+298x^29+178x^30+44x^31+76x^32+18x^33+8x^34+2x^36+1x^40

The gray image is a code over GF(2) with n=96, k=14 and d=32.
This code was found by Heurico 1.16 in 3.11 seconds.