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

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+34x^78+52x^79+134x^80+180x^81+258x^82+286x^83+350x^84+376x^85+453x^86+538x^87+599x^88+640x^89+601x^90+670x^91+545x^92+526x^93+434x^94+334x^95+256x^96+234x^97+168x^98+120x^99+96x^100+82x^101+75x^102+44x^103+53x^104+10x^105+21x^106+4x^107+9x^108+3x^110+5x^112+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 9.22 seconds.