The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+238x^58+187x^60+212x^62+150x^64+208x^66+12x^68+12x^70+2x^74+1x^92+1x^96

The gray image is a code over GF(2) with n=248, k=10 and d=116.
This code was found by Heurico 1.16 in 1.3 seconds.