The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+80x^29+30x^30+32x^31+31x^32+80x^33+2x^46

The gray image is a code over GF(2) with n=124, k=8 and d=58.
This code was found by Heurico 1.16 in 0.00891 seconds.