The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+418x^82+814x^84+760x^86+672x^88+476x^90+348x^92+204x^94+211x^96+138x^98+22x^100+20x^102+12x^104

The gray image is a code over GF(2) with n=352, k=12 and d=164.
This code was found by Heurico 1.11 in 2.87 seconds.