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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+94x^78+12x^79+338x^80+44x^81+521x^82+140x^83+639x^84+244x^85+754x^86+396x^87+837x^88+380x^89+914x^90+348x^91+679x^92+316x^93+437x^94+120x^95+366x^96+40x^97+232x^98+8x^99+141x^100+106x^102+57x^104+12x^106+12x^108+1x^110+1x^112+1x^114+1x^124

The gray image is a code over GF(2) with n=356, k=13 and d=156.
This code was found by Heurico 1.16 in 8.96 seconds.