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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+136x^54+16x^55+293x^56+112x^57+302x^58+336x^59+247x^60+560x^61+226x^62+560x^63+241x^64+336x^65+192x^66+112x^67+166x^68+16x^69+128x^70+63x^72+34x^74+11x^76+6x^78+1x^80+1x^96

The gray image is a code over GF(2) with n=248, k=12 and d=108.
This code was found by Heurico 1.16 in 1.32 seconds.