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

generates a code of length 53 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+119x^44+80x^46+405x^48+560x^50+930x^52+848x^54+625x^56+272x^58+163x^60+32x^62+35x^64+20x^68+5x^72+1x^80

The gray image is a code over GF(2) with n=212, k=12 and d=88.
This code was found by Heurico 1.16 in 1.15 seconds.