The generator matrix

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

generates a code of length 30 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+202x^24+1086x^25+3569x^26+7484x^27+15762x^28+22850x^29+28877x^30+23084x^31+16183x^32+7462x^33+3189x^34+916x^35+298x^36+86x^37+11x^38+4x^39+2x^40+4x^41+2x^42

The gray image is a code over GF(2) with n=240, k=17 and d=96.
This code was found by Heurico 1.16 in 51.4 seconds.