The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+66x^55+218x^56+196x^57+382x^58+260x^59+451x^60+272x^61+513x^62+272x^63+444x^64+248x^65+337x^66+140x^67+148x^68+36x^69+34x^70+18x^71+13x^72+12x^73+8x^74+8x^75+4x^76+4x^77+5x^78+4x^79+1x^82+1x^84

The gray image is a code over GF(2) with n=248, k=12 and d=110.
This code was found by Heurico 1.16 in 0.931 seconds.