The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+49x^76+58x^77+125x^78+140x^79+226x^80+262x^81+326x^82+396x^83+489x^84+578x^85+602x^86+698x^87+601x^88+624x^89+559x^90+520x^91+429x^92+344x^93+279x^94+224x^95+180x^96+134x^97+111x^98+60x^99+47x^100+42x^101+28x^102+10x^103+15x^104+4x^105+10x^106+10x^108+2x^109+6x^110+1x^112+1x^114+1x^122

The gray image is a code over GF(2) with n=352, k=13 and d=152.
This code was found by Heurico 1.16 in 9.23 seconds.