The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+96x^79+315x^80+470x^81+613x^82+668x^83+664x^84+622x^85+594x^86+644x^87+564x^88+520x^89+509x^90+462x^91+352x^92+314x^93+262x^94+192x^95+138x^96+54x^97+61x^98+50x^99+8x^100+4x^101+8x^102+6x^104+1x^106

The gray image is a code over GF(2) with n=348, k=13 and d=158.
This code was found by Heurico 1.16 in 4.13 seconds.