The generator matrix

 1  0  1  1  1 X+2  1  1  0  1 X+2  1  1  1  0  1 X+2  1  1  1  0  1 X+2  1  1  1  1  1  X  1  2  1  1  1  1  1 X+2  1  1  1  0  1  1  1 X+2  1  X  1  1  0  1  0  1  1  1  1  2  1  1  1  1  2
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  1  3 X+1  0  1 X+2  1  3  3  0  1 X+2  1 X+1 X+1  3  3  2  1 X+1  1 X+3  X  3 X+3 X+1  1  3  1  3  1  1 X+3  0  1  3  1  1  3  1 X+1  1 X+1  0 X+3  3  X  1  1  1  1  2
 0  0  2  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  2  2  0  0  0  2  0  2  2  2  0  2  0  2  0  0  2  0  2  0  2  2  0  2  0  2  0  0  0  0  0  0  2  0  0  2  0  2  0  2  0
 0  0  0  2  0  0  0  2  0  0  2  0  2  2  2  0  2  2  0  2  2  2  0  0  2  0  0  0  0  0  2  2  2  2  2  0  0  0  2  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  0  0  0  2  2  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  0  2  0  2  0  2  2  0  2  0  2  2  0  0  2  2  2  0  2  0  0  2  0  2  2  0  0  2  2  0  2  0  2  2  2  2  0  2  0  0  0  2  0  2  0  2  2  2  0
 0  0  0  0  0  2  0  2  0  2  0  0  2  0  2  2  2  2  0  2  0  2  2  0  2  2  2  2  0  2  0  0  0  0  0  2  2  2  0  2  2  0  2  2  0  0  2  2  0  2  2  2  0  2  0  0  2  2  2  2  0  2
 0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  0  2  2  0  2  2  2  0  2  0  0  0  2  0  0  2  0  2  2  2  2  0  0  2  0  2  2  2  0  0  0  2  0  0  0  0  0  2  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+192x^56+264x^58+403x^60+360x^62+407x^64+248x^66+128x^68+24x^70+10x^72+5x^76+3x^80+2x^88+1x^96

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 0.4 seconds.