The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+145x^76+20x^77+202x^78+124x^79+548x^80+328x^81+538x^82+504x^83+749x^84+560x^85+784x^86+560x^87+793x^88+504x^89+560x^90+328x^91+441x^92+124x^93+214x^94+20x^95+87x^96+6x^98+15x^100+22x^104+10x^108+4x^112+1x^120

The gray image is a code over GF(2) with n=344, k=13 and d=152.
This code was found by Heurico 1.16 in 6.34 seconds.