The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+94x^57+249x^58+272x^59+240x^60+222x^61+181x^62+178x^63+161x^64+106x^65+69x^66+76x^67+57x^68+46x^69+35x^70+18x^71+28x^72+8x^73+2x^74+1x^76+4x^77

The gray image is a code over GF(2) with n=248, k=11 and d=114.
This code was found by Heurico 1.11 in 0.164 seconds.