The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+160x^79+550x^80+986x^81+1232x^82+1436x^83+1793x^84+2086x^85+2268x^86+2292x^87+2515x^88+2560x^89+2275x^90+2486x^91+2281x^92+1920x^93+1737x^94+1338x^95+1078x^96+646x^97+375x^98+322x^99+218x^100+106x^101+47x^102+26x^103+12x^104+16x^105+2x^106+4x^107

The gray image is a code over GF(2) with n=356, k=15 and d=158.
This code was found by Heurico 1.13 in 22.8 seconds.