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

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+146x^79+294x^80+436x^81+601x^82+576x^83+657x^84+674x^85+638x^86+640x^87+574x^88+606x^89+549x^90+410x^91+373x^92+342x^93+188x^94+152x^95+123x^96+72x^97+56x^98+22x^99+19x^100+6x^101+13x^102+6x^103+4x^104+6x^105+2x^106+3x^108+2x^109+1x^110

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 5.38 seconds.