The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+74x^56+164x^57+197x^58+152x^59+214x^60+200x^61+149x^62+180x^63+149x^64+196x^65+141x^66+112x^67+52x^68+16x^69+11x^70+4x^71+17x^72+8x^74+1x^76+4x^78+3x^80+2x^82+1x^84

The gray image is a code over GF(2) with n=248, k=11 and d=112.
This code was found by Heurico 1.16 in 0.323 seconds.