The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+127x^28+144x^30+128x^32+80x^34+27x^36+3x^40+2x^44

The gray image is a code over GF(2) with n=124, k=9 and d=56.
This code was found by Heurico 1.16 in 0.0143 seconds.