The generator matrix

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

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+45x^82+168x^83+242x^84+218x^85+258x^86+210x^87+131x^88+156x^89+118x^90+86x^91+91x^92+102x^93+44x^94+34x^95+32x^96+24x^97+29x^98+10x^99+20x^100+12x^101+10x^102+4x^103+2x^104+1x^108

The gray image is a code over GF(2) with n=352, k=11 and d=164.
This code was found by Heurico 1.16 in 0.603 seconds.