The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+32x^76+42x^77+112x^78+172x^79+226x^80+420x^81+284x^82+684x^83+448x^84+800x^85+465x^86+876x^87+488x^88+836x^89+427x^90+636x^91+243x^92+438x^93+200x^94+184x^95+64x^96+24x^97+24x^98+8x^99+15x^100+10x^102+10x^104+7x^106+5x^108+4x^110+3x^112+2x^114+1x^116+1x^118

The gray image is a code over GF(2) with n=348, k=13 and d=152.
This code was found by Heurico 1.16 in 6.41 seconds.