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

generates a code of length 90 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+41x^78+54x^79+138x^80+126x^81+282x^82+204x^83+453x^84+216x^85+729x^86+234x^87+992x^88+234x^89+1057x^90+224x^91+932x^92+204x^93+653x^94+174x^95+385x^96+158x^97+211x^98+96x^99+123x^100+76x^101+73x^102+34x^103+33x^104+10x^105+16x^106+4x^107+10x^108+7x^110+2x^112+1x^114+2x^116+1x^120+1x^122+1x^126

The gray image is a code over GF(2) with n=360, k=13 and d=156.
This code was found by Heurico 1.16 in 9.32 seconds.