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  X  1  X  1  X  X  1  1  1  0  1  1  2  0  1  X  1  1  0  2  X  1  1  X  X  1  2  1  X  1  2
 0  X  0  0  0  X X+2  X  0  2  2  0  X X+2  X X+2 X+2 X+2 X+2  2  0  0 X+2  2 X+2  0  2  X  X  2  X  0  X  X X+2  2  X  X  2  X  2  0  0  X  0  2  0  2  0  0  2  X  0  0  X X+2  X  X X+2  X  2  0
 0  0  X  0  X  X X+2  0  0  0 X+2 X+2  X  X  2  0  X  2  0 X+2 X+2  2 X+2  2  0  2  X  2  X  X  X  0  2  0  0  X  X  X  0  2  0  0 X+2 X+2  X  0 X+2  X  2  X  X  X  2  X  0 X+2  0 X+2 X+2  X X+2  X
 0  0  0  X  X  0 X+2  X  2 X+2  X  2  2  X  X  2  0 X+2  0  X  2  X  X  0  0  X  2 X+2 X+2  X  X X+2 X+2  X X+2  0  0  0  2  0  X  0  X  0  2  0  2  2  X  0 X+2  2  X X+2 X+2 X+2  X X+2 X+2 X+2  2  X
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  2  0  2  2  2  0  0  0  0  0  0  2  0  0  0  0  2  2  0  2  2  0  0  0  2  2  2  2  0  0  2  2  2  0  2  2  0  0
 0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  0  2  2  2  0  0  2  0  2  2  0  2  0  0  2  0  2  0  2  0  0  2  0  2  2  0  0  2  0  2  0  2  0  2  0  0  2  2  0  2  2  2  2  2  0
 0  0  0  0  0  0  2  2  2  2  0  0  2  0  0  0  0  0  2  0  2  0  2  2  2  2  2  2  0  0  0  0  0  0  2  2  0  2  0  2  0  0  2  2  0  0  2  2  0  0  2  2  2  2  0  0  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 54.

Homogenous weight enumerator: w(x)=1x^0+164x^54+8x^55+316x^56+88x^57+391x^58+128x^59+433x^60+320x^61+534x^62+200x^63+489x^64+216x^65+307x^66+48x^67+213x^68+16x^69+109x^70+61x^72+26x^74+21x^76+5x^78+1x^80+1x^92

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 4.16 seconds.