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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+256x^81+299x^82+506x^83+319x^84+498x^85+269x^86+360x^87+218x^88+390x^89+133x^90+194x^91+129x^92+118x^93+66x^94+120x^95+47x^96+58x^97+30x^98+48x^99+22x^100+8x^101+3x^102+4x^103

The gray image is a code over GF(2) with n=348, k=12 and d=162.
This code was found by Heurico 1.11 in 42.7 seconds.