The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+120x^81+344x^82+400x^83+701x^84+548x^85+685x^86+586x^87+716x^88+552x^89+683x^90+382x^91+521x^92+456x^93+480x^94+312x^95+248x^96+116x^97+139x^98+58x^99+50x^100+22x^101+24x^102+18x^103+3x^104+8x^105+10x^106+4x^107+2x^109+3x^110

The gray image is a code over GF(2) with n=356, k=13 and d=162.
This code was found by Heurico 1.16 in 5.61 seconds.