The generator matrix

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

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+58x^79+193x^80+414x^81+564x^82+880x^83+932x^84+1076x^85+1222x^86+1114x^87+1301x^88+1188x^89+1304x^90+1238x^91+1086x^92+1018x^93+783x^94+640x^95+473x^96+328x^97+176x^98+142x^99+84x^100+58x^101+32x^102+20x^103+21x^104+14x^105+12x^106+4x^107+2x^108+3x^110+3x^112

The gray image is a code over GF(2) with n=356, k=14 and d=158.
This code was found by Heurico 1.16 in 19.5 seconds.