The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+64x^51+178x^52+234x^53+323x^54+458x^55+398x^56+858x^57+469x^58+1758x^59+451x^60+2762x^61+480x^62+2790x^63+498x^64+1770x^65+476x^66+912x^67+351x^68+376x^69+222x^70+198x^71+139x^72+76x^73+74x^74+26x^75+32x^76+4x^77+2x^78+2x^79+1x^82+1x^94

The gray image is a code over GF(2) with n=248, k=14 and d=102.
This code was found by Heurico 1.16 in 19.7 seconds.