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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+18x^77+88x^78+106x^79+185x^80+178x^81+354x^82+196x^83+606x^84+212x^85+838x^86+236x^87+1087x^88+218x^89+1060x^90+204x^91+785x^92+226x^93+519x^94+162x^95+302x^96+126x^97+158x^98+92x^99+69x^100+40x^101+34x^102+24x^103+21x^104+6x^105+8x^106+4x^107+11x^108+8x^110+4x^112+4x^114+1x^116+1x^126

The gray image is a code over GF(2) with n=356, k=13 and d=154.
This code was found by Heurico 1.16 in 9.23 seconds.